<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019e2171-b9d5-7049-a408-5ec2c1393361,g:72894df9-4a89-4f06-a242-4f5c4b8b7592-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="https://xbrl.org/2023/arcrole/summation-item" xlink:type="simple" xlink:href="https://www.xbrl.org/2023/calculation-1.1.xsd#summation-item"/>
  <link:roleRef roleURI="http://www.papajohns.com/role/CondensedConsolidatedBalanceSheets" xlink:type="simple" xlink:href="pzza-20260628.xsd#CondensedConsolidatedBalanceSheets"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/CondensedConsolidatedBalanceSheets" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7dbc-a6a8-5fbe6af64b4d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7dbc-a6a8-5fbe6af64b4d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset_019e2171-bc6e-75b2-8b57-6f299615d1ad" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAsset_019e2171-bc6e-75b2-8b57-6f299615d1ad" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill_019e2171-bc6e-7158-b0d4-20762a7c96d1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_Goodwill_019e2171-bc6e-7158-b0d4-20762a7c96d1" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset_019e2171-bc6e-7033-98a6-0c715cfdfb0f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_FinanceLeaseRightOfUseAsset_019e2171-bc6e-7033-98a6-0c715cfdfb0f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet_019e2171-bc6e-7984-a787-6205c39c1b5d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_PropertyPlantAndEquipmentNet_019e2171-bc6e-7984-a787-6205c39c1b5d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent_019e2171-bc6e-776a-9008-5f775baac8e6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent_019e2171-bc6e-776a-9008-5f775baac8e6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent_019e2171-bc6e-7fcb-9f43-c7470bd0758b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bc6e-7055-b187-e434fee34e6c" xlink:to="loc_us-gaap_OtherAssetsNoncurrent_019e2171-bc6e-7fcb-9f43-c7470bd0758b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e2171-bc6e-7e5c-9a0d-ff6a09352fcd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019e2171-bc6e-7da8-a265-fa8085400e00" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e2171-bc6e-7e5c-9a0d-ff6a09352fcd" xlink:to="loc_us-gaap_StockholdersEquity_019e2171-bc6e-7da8-a265-fa8085400e00" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest_019e2171-bc6e-759e-8d8d-57fcd1be7a55" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e2171-bc6e-7e5c-9a0d-ff6a09352fcd" xlink:to="loc_us-gaap_MinorityInterest_019e2171-bc6e-759e-8d8d-57fcd1be7a55" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e2171-bc6e-75d2-bc8a-a67a05be0a38" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_019e2171-bc6e-719a-a923-2b23cb15c065" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e2171-bc6e-75d2-bc8a-a67a05be0a38" xlink:to="loc_us-gaap_Liabilities_019e2171-bc6e-719a-a923-2b23cb15c065" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_019e2171-bc6e-767d-8615-a2d02981ee91" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e2171-bc6e-75d2-bc8a-a67a05be0a38" xlink:to="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_019e2171-bc6e-767d-8615-a2d02981ee91" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e2171-bc6e-744a-b16f-38702af2b88a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity_019e2171-bc6e-75d2-bc8a-a67a05be0a38" xlink:to="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e2171-bc6e-744a-b16f-38702af2b88a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue_019e2171-bc6e-7426-a5b8-f2341d093f06" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:to="loc_us-gaap_CommonStockValue_019e2171-bc6e-7426-a5b8-f2341d093f06" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital_019e2171-bc6e-7016-8df2-5bd8c771412c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:to="loc_us-gaap_AdditionalPaidInCapital_019e2171-bc6e-7016-8df2-5bd8c771412c" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e2171-bc6e-79a1-bf54-c637b84e19d9" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e2171-bc6e-79a1-bf54-c637b84e19d9" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit_019e2171-bc6e-78ec-9d9c-09c506f88ef6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:to="loc_us-gaap_RetainedEarningsAccumulatedDeficit_019e2171-bc6e-78ec-9d9c-09c506f88ef6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue_019e2171-bc6e-7777-a481-e9b12a450cea" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_StockholdersEquity_019e2171-bc6e-74ca-b59b-6905b6b79076" xlink:to="loc_us-gaap_TreasuryStockCommonValue_019e2171-bc6e-7777-a481-e9b12a450cea" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e2171-bc6e-7525-aee8-678496b43f67" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e2171-bc6e-7525-aee8-678496b43f67" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent_019e2171-bc6e-735d-9cb5-3bbfc91e4b69" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_AccountsReceivableNetCurrent_019e2171-bc6e-735d-9cb5-3bbfc91e4b69" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossCurrent_019e2171-bc6e-71d3-ab31-227802960041" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossCurrent_019e2171-bc6e-71d3-ab31-227802960041" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReceivable_019e2171-bc6e-75b7-a404-626da25c8ff6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReceivable"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_IncomeTaxReceivable_019e2171-bc6e-75b7-a404-626da25c8ff6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet_019e2171-bc6e-7f14-8139-f636e24c799a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryNet"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_InventoryNet_019e2171-bc6e-7f14-8139-f636e24c799a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e2171-bc6e-7e83-ad1b-5dca84dab247" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e2171-bc6e-7e83-ad1b-5dca84dab247" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bc6e-74eb-bb8a-72f652143a19" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bc6e-7a6a-b257-757d9d5606c2" xlink:to="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bc6e-74eb-bb8a-72f652143a19" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent_019e2171-bc6e-7296-8908-75691f30db25" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_AccountsPayableCurrent_019e2171-bc6e-7296-8908-75691f30db25" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrent_019e2171-bc6e-7aca-ad0e-870978d2917a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxesPayableCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_TaxesPayableCurrent_019e2171-bc6e-7aca-ad0e-870978d2917a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019e2171-bc6e-717a-ac4b-f40cfb1e45cf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019e2171-bc6e-717a-ac4b-f40cfb1e45cf" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent_019e2171-bc6e-7699-b870-f9a222387426" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_ContractWithCustomerLiabilityCurrent_019e2171-bc6e-7699-b870-f9a222387426" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityCurrent_019e2171-bc6e-78f8-859f-661dcaf3760d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityCurrent"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_FinanceLeaseLiabilityCurrent_019e2171-bc6e-78f8-859f-661dcaf3760d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent_019e2171-bc6e-7d4e-b82c-130fffce04d6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrent_019e2171-bc6e-7d4e-b82c-130fffce04d6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent_019e2171-bc6e-7f95-86db-d16e79c51bc3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_LongTermDebtCurrent_019e2171-bc6e-7f95-86db-d16e79c51bc3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019f4560-ec37-7e82-b6dd-038810877747" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-75fa-bada-46266ff7d459" xlink:to="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019f4560-ec37-7e82-b6dd-038810877747" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-7b08-addc-c54200ea51c9" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_LiabilitiesCurrent_019e2171-bc6e-7b08-addc-c54200ea51c9" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityNoncurrent_019e2171-bc6e-7cab-93cf-927cd88275c7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityNoncurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_ContractWithCustomerLiabilityNoncurrent_019e2171-bc6e-7cab-93cf-927cd88275c7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrent_019e2171-bc6e-70a6-a209-4bce198c2157" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_FinanceLeaseLiabilityNoncurrent_019e2171-bc6e-70a6-a209-4bce198c2157" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019e2171-bc6e-7603-a5dc-4ee56b93ebba" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019e2171-bc6e-7603-a5dc-4ee56b93ebba" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent_019e2171-bc6e-7835-8319-7d916bf60b6f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_LongTermDebtNoncurrent_019e2171-bc6e-7835-8319-7d916bf60b6f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent_019e2171-bc6e-713a-a17d-771caaf71fd4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Liabilities_019e2171-bc6e-7020-b64a-62499a17dceb" xlink:to="loc_us-gaap_OtherLiabilitiesNoncurrent_019e2171-bc6e-713a-a17d-771caaf71fd4" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/CondensedConsolidatedStatementsofOperations" xlink:type="simple" xlink:href="pzza-20260628.xsd#CondensedConsolidatedStatementsofOperations"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/CondensedConsolidatedStatementsofOperations" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_019e2171-bd45-78aa-8f9c-f54014cf1457" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e2171-bd45-7d81-974b-b6db59e375fa" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_019e2171-bd45-78aa-8f9c-f54014cf1457" xlink:to="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e2171-bd45-7d81-974b-b6db59e375fa" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7ec6-b78f-4a8ca9a514cd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostsAndExpenses"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OperatingIncomeLoss_019e2171-bd45-78aa-8f9c-f54014cf1457" xlink:to="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7ec6-b78f-4a8ca9a514cd" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7745-9231-0bd173bf4c52" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostsAndExpenses"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostDepreciationAmortizationAndDepletion_019e2171-bd45-7a67-ae1c-2b6bc32b0053" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostDepreciationAmortizationAndDepletion"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7745-9231-0bd173bf4c52" xlink:to="loc_us-gaap_CostDepreciationAmortizationAndDepletion_019e2171-bd45-7a67-ae1c-2b6bc32b0053" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense_019e2171-bd45-71f5-8258-68607d2a70c7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingExpense"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7745-9231-0bd173bf4c52" xlink:to="loc_us-gaap_AdvertisingExpense_019e2171-bd45-71f5-8258-68607d2a70c7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_019e2171-bd45-7068-bbc3-63dd4620bfe0" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7745-9231-0bd173bf4c52" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_019e2171-bd45-7068-bbc3-63dd4620bfe0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_019e2171-bd45-772e-ac38-9b665b7e60cb" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CostsAndExpenses_019e2171-bd45-7745-9231-0bd173bf4c52" xlink:to="loc_us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_019e2171-bd45-772e-ac38-9b665b7e60cb" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e2171-bd45-7cf5-9ee4-9178bf33591a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_019e2171-bd45-7104-afbc-7a7c7f47e53a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_019e2171-bd45-7cf5-9ee4-9178bf33591a" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_019e2171-bd45-7104-afbc-7a7c7f47e53a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd45-7946-beae-5dd375815ae4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ProfitLoss_019e2171-bd45-7cf5-9ee4-9178bf33591a" xlink:to="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd45-7946-beae-5dd375815ae4" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd45-74ac-ab3c-f76b20237449" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss_019e2171-bd45-7897-a666-88c66e9b4d54" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd45-74ac-ab3c-f76b20237449" xlink:to="loc_us-gaap_OperatingIncomeLoss_019e2171-bd45-7897-a666-88c66e9b4d54" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_019e2171-bd45-7334-9adf-4cccf7eb466e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd45-74ac-ab3c-f76b20237449" xlink:to="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_019e2171-bd45-7334-9adf-4cccf7eb466e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_019e2171-bd45-776f-9580-2aa08c48c64f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e2171-bd45-7202-a20e-7fbb1b7c19cb" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_019e2171-bd45-776f-9580-2aa08c48c64f" xlink:to="loc_us-gaap_ProfitLoss_019e2171-bd45-7202-a20e-7fbb1b7c19cb" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e2171-bd45-7d4a-9955-ee21c6618036" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLoss_019e2171-bd45-776f-9580-2aa08c48c64f" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e2171-bd45-7d4a-9955-ee21c6618036" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/CondensedConsolidatedStatementsofComprehensiveIncome" xlink:type="simple" xlink:href="pzza-20260628.xsd#CondensedConsolidatedStatementsofComprehensiveIncome"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/CondensedConsolidatedStatementsofComprehensiveIncome" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e2171-bd45-79fd-8c7d-0715427ac36f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e2171-bd45-75b8-8662-2aed140ddcc6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e2171-bd45-79fd-8c7d-0715427ac36f" xlink:to="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e2171-bd45-75b8-8662-2aed140ddcc6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax_019e2171-bd45-7dbf-9330-1f78682b2066" xlink:href="pzza-20260628.xsd#pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e2171-bd45-79fd-8c7d-0715427ac36f" xlink:to="loc_pzza_NetIncomeLossAttributableToRedeemableNoncontrollingInterestNetOfTax_019e2171-bd45-7dbf-9330-1f78682b2066" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_019e2171-bd45-7153-8e14-5ec3065a82b3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax_019e2171-bd45-79fd-8c7d-0715427ac36f" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_019e2171-bd45-7153-8e14-5ec3065a82b3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e2171-bd45-7453-8ee0-18432b062ee8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e2171-bd45-75ca-acd0-f8dd5e514989" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e2171-bd45-7453-8ee0-18432b062ee8" xlink:to="loc_us-gaap_ProfitLoss_019e2171-bd45-75ca-acd0-f8dd5e514989" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e2171-bd45-70e5-9eea-ed45f9ae5c5e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e2171-bd45-7453-8ee0-18432b062ee8" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e2171-bd45-70e5-9eea-ed45f9ae5c5e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e2171-bd45-7550-8c23-41dd26c48d1d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax_019e2171-bd45-7ce6-ac10-3e55695b8d4f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e2171-bd45-7550-8c23-41dd26c48d1d" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax_019e2171-bd45-7ce6-ac10-3e55695b8d4f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTax_019e2171-bd45-781d-aabc-e38dab9bd3a4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossTax"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e2171-bd45-7550-8c23-41dd26c48d1d" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossTax_019e2171-bd45-781d-aabc-e38dab9bd3a4" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax_019e2171-bd45-71e2-a0a1-8660939d3885" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax_019e2171-bd45-77eb-956e-bc6826afd165" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax_019e2171-bd45-71e2-a0a1-8660939d3885" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentBeforeTax_019e2171-bd45-77eb-956e-bc6826afd165" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTax_019e2171-bd45-75b1-92a1-e9d48b990853" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax_019e2171-bd45-71e2-a0a1-8660939d3885" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationBeforeTax_019e2171-bd45-75b1-92a1-e9d48b990853" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTax_019e2171-bd45-7048-83ff-de7d8a889d42" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossTax"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_019e2171-bd45-7fbe-b0d1-226cbe7d3b9b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTax_019e2171-bd45-7048-83ff-de7d8a889d42" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_019e2171-bd45-7fbe-b0d1-226cbe7d3b9b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax_019e2171-bd45-7cd8-a45f-a5a523e29f97" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTax_019e2171-bd45-7048-83ff-de7d8a889d42" xlink:to="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationTax_019e2171-bd45-7cd8-a45f-a5a523e29f97" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/CondensedConsolidatedStatementsofCashFlows" xlink:type="simple" xlink:href="pzza-20260628.xsd#CondensedConsolidatedStatementsofCashFlows"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/CondensedConsolidatedStatementsofCashFlows" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2171-bd45-710e-b99e-5e8c12d18ee5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-7867-bf3c-612b3119aae5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2171-bd45-710e-b99e-5e8c12d18ee5" xlink:to="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-7867-bf3c-612b3119aae5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7b24-b34f-39096e7c1e8b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2171-bd45-710e-b99e-5e8c12d18ee5" xlink:to="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7b24-b34f-39096e7c1e8b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7e15-9f15-785df5509020" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2171-bd45-710e-b99e-5e8c12d18ee5" xlink:to="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7e15-9f15-785df5509020" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e2171-bd45-7a19-84bb-84428bcd38f1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2171-bd45-710e-b99e-5e8c12d18ee5" xlink:to="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e2171-bd45-7a19-84bb-84428bcd38f1" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_019e2171-bd45-7191-bb42-bf18119518db" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromRepaymentsOfLinesOfCredit"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_019e2171-bd45-7191-bb42-bf18119518db" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfSecuredDebt_019e2171-bd45-7f2a-83c6-984f5726ee05" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromRepaymentsOfSecuredDebt"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_ProceedsFromRepaymentsOfSecuredDebt_019e2171-bd45-7f2a-83c6-984f5726ee05" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts_019e2171-bd45-7f88-b17c-4eaac4b61c26" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_PaymentsOfDebtIssuanceCosts_019e2171-bd45-7f88-b17c-4eaac4b61c26" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromStockOptionsExercised_019e2171-bd45-72c3-8fd1-1ef1d969c89d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_ProceedsFromStockOptionsExercised_019e2171-bd45-72c3-8fd1-1ef1d969c89d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock_019e2171-bd45-796c-a9bf-bacd01e613b0" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_PaymentsOfDividendsCommonStock_019e2171-bd45-796c-a9bf-bacd01e613b0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019e2171-bd45-7092-b246-a767f8cadd0d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:calculationArc order="6" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019e2171-bd45-7092-b246-a767f8cadd0d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToMinorityShareholders_019e2171-bd45-7692-87f4-dbadb071e624" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToMinorityShareholders"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_PaymentsToMinorityShareholders_019e2171-bd45-7692-87f4-dbadb071e624" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments_019e2171-bd45-7819-a318-f653f972e6f7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:calculationArc order="8" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_FinanceLeasePrincipalPayments_019e2171-bd45-7819-a318-f653f972e6f7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_019f6e9e-021e-72d7-a53a-0ef893f7dba1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:calculationArc order="9" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2171-bd45-7fc1-91da-38382926ee6b" xlink:to="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_019f6e9e-021e-72d7-a53a-0ef893f7dba1" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019e2171-bd45-77a7-a4ea-e1c9664533c5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019e2171-bd45-77a7-a4ea-e1c9664533c5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_PaymentsToAcquirePropertyAndEquipmentRelatedToLossFromNaturalDisaster_019e2171-bd45-7bd1-a1c6-640154086a3e" xlink:href="pzza-20260628.xsd#pzza_PaymentsToAcquirePropertyAndEquipmentRelatedToLossFromNaturalDisaster"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_pzza_PaymentsToAcquirePropertyAndEquipmentRelatedToLossFromNaturalDisaster_019e2171-bd45-7bd1-a1c6-640154086a3e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_019e2171-bd45-7ad9-b32b-499356ba028c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromInsuranceSettlementInvestingActivities"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_019e2171-bd45-7ad9-b32b-499356ba028c" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfNotesReceivable_019e2171-bd45-77d0-8789-3b91c641ba77" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromCollectionOfNotesReceivable"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_us-gaap_ProceedsFromCollectionOfNotesReceivable_019e2171-bd45-77d0-8789-3b91c641ba77" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_019e2171-bd45-7569-9792-eb88fd5bb355" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_019e2171-bd45-7569-9792-eb88fd5bb355" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_ProceedsFromInvestments_019e2171-bd45-7cb6-9797-b9482e0e9412" xlink:href="pzza-20260628.xsd#pzza_ProceedsFromInvestments"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_pzza_ProceedsFromInvestments_019e2171-bd45-7cb6-9797-b9482e0e9412" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_019e2171-bd45-7423-b445-84d1f64d8d50" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2171-bd45-7d30-a73e-96ba7b71dfb4" xlink:to="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_019e2171-bd45-7423-b445-84d1f64d8d50" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_019e2171-bd45-7a28-846a-d272ec33eb83" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_ProfitLoss_019e2171-bd45-7a28-846a-d272ec33eb83" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForDoubtfulAccounts_019e2171-bd45-7cc1-aef4-2256b6e7e197" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_ProvisionForDoubtfulAccounts_019e2171-bd45-7cc1-aef4-2256b6e7e197" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization_019e2171-bd45-735a-8d03-270f8fd37182" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_DepreciationDepletionAndAmortization_019e2171-bd45-735a-8d03-270f8fd37182" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_019e2171-bd45-72b8-a575-25c80cb74140" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_DeferredIncomeTaxExpenseBenefit_019e2171-bd45-72b8-a575-25c80cb74140" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation_019e2171-bd45-7685-b6e2-3491a6a31147" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_ShareBasedCompensation_019e2171-bd45-7685-b6e2-3491a6a31147" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_RefranchisingAndImpairmentGainLoss_019e2171-bd45-7fa3-90bc-55a96ca0fd87" xlink:href="pzza-20260628.xsd#pzza_RefranchisingAndImpairmentGainLoss"/>
    <link:calculationArc order="6" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_pzza_RefranchisingAndImpairmentGainLoss_019e2171-bd45-7fa3-90bc-55a96ca0fd87" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019e2171-bd45-77b5-a90b-76a75504133b" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019e2171-bd45-77b5-a90b-76a75504133b" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense_019e2171-bd45-7b90-bfc9-ca4d10b8fe88" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:calculationArc order="8" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_OtherNoncashIncomeExpense_019e2171-bd45-7b90-bfc9-ca4d10b8fe88" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable_019e2171-bd45-73cf-a71e-cf7233060a7a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:calculationArc order="9" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInAccountsReceivable_019e2171-bd45-73cf-a71e-cf7233060a7a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInIncomeTaxesReceivable_019e2171-bd45-7338-8d6b-03bdfcf96df8" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInIncomeTaxesReceivable"/>
    <link:calculationArc order="10" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInIncomeTaxesReceivable_019e2171-bd45-7338-8d6b-03bdfcf96df8" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInventories_019e2171-bd45-76ed-9379-f5dde46e344a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInventories"/>
    <link:calculationArc order="11" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInInventories_019e2171-bd45-76ed-9379-f5dde46e344a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019e2171-bd45-7e4c-8a03-fcaa34ab94a6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:calculationArc order="12" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019e2171-bd45-7e4c-8a03-fcaa34ab94a6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_019e2171-bd45-7e40-95ae-8b0fecf0cba7" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet"/>
    <link:calculationArc order="13" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_019e2171-bd45-7e40-95ae-8b0fecf0cba7" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable_019e2171-bd45-7cda-9f56-89d38da261e3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:calculationArc order="14" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInAccountsPayable_019e2171-bd45-7cda-9f56-89d38da261e3" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedTaxesPayable_019e2171-bd45-71ad-8f02-17fc8539fd6a" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedTaxesPayable"/>
    <link:calculationArc order="15" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInAccruedTaxesPayable_019e2171-bd45-71ad-8f02-17fc8539fd6a" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e2171-bd45-74cc-ab17-e409493f20cf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:calculationArc order="16" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e2171-bd45-74cc-ab17-e409493f20cf" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_IncreaseDecreaseInContractLiabilities_019e2171-bd45-7139-9796-3e13199273fc" xlink:href="pzza-20260628.xsd#pzza_IncreaseDecreaseInContractLiabilities"/>
    <link:calculationArc order="17" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_pzza_IncreaseDecreaseInContractLiabilities_019e2171-bd45-7139-9796-3e13199273fc" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_IncreaseDecreaseInAdvertisingFundAssetsAndLiabilities_019e2171-bd45-7469-8f8e-b0afbe3ea51c" xlink:href="pzza-20260628.xsd#pzza_IncreaseDecreaseInAdvertisingFundAssetsAndLiabilities"/>
    <link:calculationArc order="18" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2171-bd45-79a2-a7ff-45889b79bbbf" xlink:to="loc_pzza_IncreaseDecreaseInAdvertisingFundAssetsAndLiabilities_019e2171-bd45-7469-8f8e-b0afbe3ea51c" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/SignificantAccountingPoliciesNarrativeDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#SignificantAccountingPoliciesNarrativeDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/SignificantAccountingPoliciesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_pzza_ProceedsFromInsuranceSettlementOperatingAndInvestingActivities_019e2171-bd45-7755-aff2-65056a4790e3" xlink:href="pzza-20260628.xsd#pzza_ProceedsFromInsuranceSettlementOperatingAndInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInsuranceSettlementOperatingActivities_019e2171-bd45-77b3-8eb6-716b77089770" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromInsuranceSettlementOperatingActivities"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_ProceedsFromInsuranceSettlementOperatingAndInvestingActivities_019e2171-bd45-7755-aff2-65056a4790e3" xlink:to="loc_us-gaap_ProceedsFromInsuranceSettlementOperatingActivities_019e2171-bd45-77b3-8eb6-716b77089770" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_019e2171-bd45-7bc1-a16d-4a0d2bdb670f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromInsuranceSettlementInvestingActivities"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_ProceedsFromInsuranceSettlementOperatingAndInvestingActivities_019e2171-bd45-7755-aff2-65056a4790e3" xlink:to="loc_us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_019e2171-bd45-7bc1-a16d-4a0d2bdb670f" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/SignificantAccountingPoliciesNetIncomeLossAttributabletoJointVenturesDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#SignificantAccountingPoliciesNetIncomeLossAttributabletoJointVenturesDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/SignificantAccountingPoliciesNetIncomeLossAttributabletoJointVenturesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperations_019e2171-bd45-79d2-9dac-8d954bee435f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperations"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_019e2171-bd45-78d8-857b-abdc01ebf294" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations_019e2171-bd45-79d2-9dac-8d954bee435f" xlink:to="loc_us-gaap_NetIncomeLoss_019e2171-bd45-78d8-857b-abdc01ebf294" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_019e2171-bd45-743c-b36c-524e21d1b7ce" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations_019e2171-bd45-79d2-9dac-8d954bee435f" xlink:to="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_019e2171-bd45-743c-b36c-524e21d1b7ce" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_019e2171-bd45-75ee-8eba-a3f89fbc4637" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations_019e2171-bd45-79d2-9dac-8d954bee435f" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNonredeemableNoncontrollingInterest_019e2171-bd45-75ee-8eba-a3f89fbc4637" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/PapaJohnsMarketingFundIncDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#PapaJohnsMarketingFundIncDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/PapaJohnsMarketingFundIncDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e2171-bd46-7b39-88a6-3b7e96f9e915" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e2171-bd46-718a-85ec-11920f54afcc" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bd46-7b39-88a6-3b7e96f9e915" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e2171-bd46-718a-85ec-11920f54afcc" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent_019e2171-bd46-7a40-99c3-7fa233ab831e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bd46-7b39-88a6-3b7e96f9e915" xlink:to="loc_us-gaap_AccountsReceivableNetCurrent_019e2171-bd46-7a40-99c3-7fa233ab831e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e2171-bd46-7170-87df-54f7b40207fa" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bd46-7b39-88a6-3b7e96f9e915" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019e2171-bd46-7170-87df-54f7b40207fa" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReceivable_019e2171-bd46-7ee5-a381-dcced0680d3f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReceivable"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsCurrent_019e2171-bd46-7b39-88a6-3b7e96f9e915" xlink:to="loc_us-gaap_IncomeTaxReceivable_019e2171-bd46-7ee5-a381-dcced0680d3f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_019e2171-bd46-71a0-bdd9-65f1d18422e4" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet_019e2171-bd46-7c57-ab95-f8d24dfa8572" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bd46-71a0-bdd9-65f1d18422e4" xlink:to="loc_us-gaap_DeferredIncomeTaxAssetsNet_019e2171-bd46-7c57-ab95-f8d24dfa8572" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent_019e2171-bd46-7a8a-99f7-3fb6afd6e508" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bd46-71a0-bdd9-65f1d18422e4" xlink:to="loc_us-gaap_AssetsCurrent_019e2171-bd46-7a8a-99f7-3fb6afd6e508" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent_019e2171-bd46-782f-a6b0-a1051cdc1d68" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_Assets_019e2171-bd46-71a0-bdd9-65f1d18422e4" xlink:to="loc_us-gaap_OtherAssetsNoncurrent_019e2171-bd46-782f-a6b0-a1051cdc1d68" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/EarningsperShareDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#EarningsperShareDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/EarningsperShareDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e2171-bd46-7344-a619-6a5cf8c5ee68" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_019e2171-bd46-7635-b261-836402046f14" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e2171-bd46-7344-a619-6a5cf8c5ee68" xlink:to="loc_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_019e2171-bd46-7635-b261-836402046f14" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_019e2171-bd46-71a5-bd36-54cd4c93fe5c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e2171-bd46-7344-a619-6a5cf8c5ee68" xlink:to="loc_us-gaap_NetIncomeLoss_019e2171-bd46-71a5-bd36-54cd4c93fe5c" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e2171-bd46-7b6d-8b34-624c1295890e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e2171-bd46-74c1-948b-9e93a3d6fbad" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e2171-bd46-7b6d-8b34-624c1295890e" xlink:to="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e2171-bd46-74c1-948b-9e93a3d6fbad" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019e2171-bd46-7c23-a4b6-77aa38449d06" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e2171-bd46-7b6d-8b34-624c1295890e" xlink:to="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019e2171-bd46-7c23-a4b6-77aa38449d06" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/DivestituresAssetsandLiabilitiesWithJointVentureClassifiedasHeldforSaleDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#DivestituresAssetsandLiabilitiesWithJointVentureClassifiedasHeldforSaleDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/DivestituresAssetsandLiabilitiesWithJointVentureClassifiedasHeldforSaleDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7533-a459-756e6f59b805" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent_019e2171-bd46-7986-b0a2-a70cdc472da5" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7533-a459-756e6f59b805" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent_019e2171-bd46-7986-b0a2-a70cdc472da5" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_019e2171-bd46-7a67-b5ff-38f0cdef3b56" xlink:href="pzza-20260628.xsd#pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7533-a459-756e6f59b805" xlink:to="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_019e2171-bd46-7a67-b5ff-38f0cdef3b56" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_019e2171-bd46-76f7-8112-9158c4a8661d" xlink:href="pzza-20260628.xsd#pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7533-a459-756e6f59b805" xlink:to="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_019e2171-bd46-76f7-8112-9158c4a8661d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7ed4-90bb-87fa517f88de" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets_019e2171-bd46-7845-b3a8-4f200992cbda" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7ed4-90bb-87fa517f88de" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets_019e2171-bd46-7845-b3a8-4f200992cbda" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipment_019e2171-bd46-7ba4-8f8d-83c7bfc688f6" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipment"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7ed4-90bb-87fa517f88de" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipment_019e2171-bd46-7ba4-8f8d-83c7bfc688f6" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRightOfUseAsset_019e2171-bd46-79f1-8497-008ebe2ddfff" xlink:href="pzza-20260628.xsd#pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRightOfUseAsset"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7ed4-90bb-87fa517f88de" xlink:to="loc_pzza_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRightOfUseAsset_019e2171-bd46-79f1-8497-008ebe2ddfff" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_019e2171-bd46-7913-bdb9-a5499a582601" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e2171-bd46-7ed4-90bb-87fa517f88de" xlink:to="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_019e2171-bd46-7913-bdb9-a5499a582601" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/SegmentInformationSegmentResultsDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#SegmentInformationSegmentResultsDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/SegmentInformationSegmentResultsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:href="pzza-20260628.xsd#pzza_AdjustedEBITDA"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_019e2171-bd46-7aeb-b0e4-eec2713b4ea0" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_019e2171-bd46-7aeb-b0e4-eec2713b4ea0" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e2171-bd46-71fd-aa61-de84257399ca" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e2171-bd46-71fd-aa61-de84257399ca" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostDirectLabor_019e2171-bd46-799f-af78-3b1a2b2bde03" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostDirectLabor"/>
    <link:calculationArc order="3" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_us-gaap_CostDirectLabor_019e2171-bd46-799f-af78-3b1a2b2bde03" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostDirectMaterial_019e2171-bd46-7a20-adad-f2499bb57a1d" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostDirectMaterial"/>
    <link:calculationArc order="4" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_us-gaap_CostDirectMaterial_019e2171-bd46-7a20-adad-f2499bb57a1d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingOtherItemAmount_019e2171-bd46-781f-9277-34c88fa0272e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_us-gaap_SegmentReportingOtherItemAmount_019e2171-bd46-781f-9277-34c88fa0272e" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_CostOther_019e2171-bd46-74c7-bd41-ae021a4797c7" xlink:href="pzza-20260628.xsd#pzza_CostOther"/>
    <link:calculationArc order="6" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_AdjustedEBITDA_019e2171-bd46-74a3-97c0-3155d123560c" xlink:to="loc_pzza_CostOther_019e2171-bd46-74c7-bd41-ae021a4797c7" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/SegmentInformationReconciliationofSegmentResultstoCompanyResultsDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#SegmentInformationReconciliationofSegmentResultstoCompanyResultsDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/SegmentInformationReconciliationofSegmentResultstoCompanyResultsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd46-780a-8660-32a4de964807" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_AdjustedEBITDA_019e2171-bd46-742a-969f-7493dc895a4d" xlink:href="pzza-20260628.xsd#pzza_AdjustedEBITDA"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd46-780a-8660-32a4de964807" xlink:to="loc_pzza_AdjustedEBITDA_019e2171-bd46-742a-969f-7493dc895a4d" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7a51-afc6-300787cfd352" xlink:href="pzza-20260628.xsd#pzza_OtherIncomeExpenseAdjustments"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd46-780a-8660-32a4de964807" xlink:to="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7a51-afc6-300787cfd352" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_019e2171-bd46-7ed4-8d76-05a65ad20faf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2171-bd46-780a-8660-32a4de964807" xlink:to="loc_us-gaap_InterestIncomeExpenseNonoperatingNet_019e2171-bd46-7ed4-8d76-05a65ad20faf" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.papajohns.com/role/SegmentInformationOtherIncomeExpenseAdjustmentsDetails" xlink:type="simple" xlink:href="pzza-20260628.xsd#SegmentInformationOtherIncomeExpenseAdjustmentsDetails"/>
  <link:calculationLink xlink:role="http://www.papajohns.com/role/SegmentInformationOtherIncomeExpenseAdjustmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:href="pzza-20260628.xsd#pzza_OtherIncomeExpenseAdjustments"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostDepreciationAmortizationAndDepletion_019e2171-bd46-733b-a6e3-54441fce6205" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostDepreciationAmortizationAndDepletion"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:to="loc_us-gaap_CostDepreciationAmortizationAndDepletion_019e2171-bd46-733b-a6e3-54441fce6205" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation_019e2171-bd46-784a-aefb-d35633d21f2c" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:to="loc_us-gaap_ShareBasedCompensation_019e2171-bd46-784a-aefb-d35633d21f2c" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_pzza_GainLossOnRefranchise_019e2171-bd46-7c85-bbbe-d43150b5b758" xlink:href="pzza-20260628.xsd#pzza_GainLossOnRefranchise"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:to="loc_pzza_GainLossOnRefranchise_019e2171-bd46-7c85-bbbe-d43150b5b758" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringSettlementAndImpairmentProvisions_019e2171-bd46-7f53-8f12-df06d7e46c3f" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringSettlementAndImpairmentProvisions"/>
    <link:calculationArc order="4" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:to="loc_us-gaap_RestructuringSettlementAndImpairmentProvisions_019e2171-bd46-7f53-8f12-df06d7e46c3f" xlink:type="arc"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCostAndExpenseOperating_019e2171-bd46-7abb-ac05-3864b3b73eef" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCostAndExpenseOperating"/>
    <link:calculationArc order="5" weight="-1.0" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="loc_pzza_OtherIncomeExpenseAdjustments_019e2171-bd46-7ce2-8e0d-03e1c637279e" xlink:to="loc_us-gaap_OtherCostAndExpenseOperating_019e2171-bd46-7abb-ac05-3864b3b73eef" xlink:type="arc"/>
  </link:calculationLink>
</link:linkbase>
