Automatic renewal interval.

No definition available.

Name:	kod_AutomaticRenewalInterval
Namespace Prefix:	kod_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Commitments and contingencies disclosure.

+ References

No definition available.

+ Details

Name:	kod_CommitmentsAndContingenciesDisclosureLineItems
Namespace Prefix:	kod_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Lessee operating lease initial term of contract.

+ References

No definition available.

+ Details

Name:	kod_LesseeOperatingLeaseInitialTermOfContract
Namespace Prefix:	kod_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Non Cash Lease Impairment Expense

+ References

No definition available.

+ Details

Name:	kod_NonCashLeaseImpairmentExpense
Namespace Prefix:	kod_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Number of leased buildings.

+ References

No definition available.

+ Details

Name:	kod_NumberOfLeasedBuildings
Namespace Prefix:	kod_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of options to extend lease term.

+ References

No definition available.

+ Details

Name:	kod_NumberOfOptionsToExtendLeaseTerm
Namespace Prefix:	kod_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Variable Sublease Income

+ References

No definition available.

+ Details

Name:	kod_VariableSubleaseIncome
Namespace Prefix:	kod_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Area of land held.

+ References

No definition available.

+ Details

Name:	us-gaap_AreaOfLand
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:areaItemType
Balance Type:	na
Period Type:	instant

- Definition

Description of terms and conditions of option to extend lessee's operating lease. Includes, but is not limited to, information about option recognized as part of right-of-use asset and lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseOptionToExtend
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Term of lessee's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of sublease income excluding finance and operating lease expense.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_SubleaseIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	srt_StatementGeographicalAxis=stpr_CA
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LeaseContractualTermAxis=kod_LeaseAgreementOnJuneTwoThousandAndTwentyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=kod_OfficeAndLaboratorySpaceMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_StatementGeographicalAxis=country_CH
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LeaseContractualTermAxis=kod_LeaseAgreementOnAprilTwoThousandAndTwentyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=kod_BuildingOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=kod_BuildingTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Commitments and Contingencies - Additional Information (Details) $ in Millions	1 Months Ended		3 Months Ended			6 Months Ended
	Jun. 30, 2020 ft² Options Building	Apr. 30, 2020 m²	Jun. 30, 2026 USD ($)	Jun. 30, 2025 USD ($)	Mar. 31, 2025 USD ($)	Jun. 30, 2026 USD ($)	Jun. 30, 2025 USD ($)
Commitments And Contingencies Disclosure [Line Items]
Non Cash Lease Impairment Expense					$ 1.9
Variable sublease income			$ 0.5	$ 0.4		$ 1.0	$ 0.6
Sublease Income			$ 1.9	$ 1.9		$ 3.8	$ 2.4
California \| Lease Agreement on June 2020
Commitments And Contingencies Disclosure [Line Items]
Initial lease term	6 years 6 months
Number of buildings leased \| Building	2
Maximum \| Lease Agreement on June 2020
Commitments And Contingencies Disclosure [Line Items]
Lease area \| ft²	83,000
Minimum \| Lease Agreement on June 2020
Commitments And Contingencies Disclosure [Line Items]
Lease area \| ft²	73,000
Rottenstrasse 5 in Visp \| Switzerland \| Lease Agreement on April 2020
Commitments And Contingencies Disclosure [Line Items]
Lease area \| m²		1,000
Initial lease term		5 years
Automatic renewal interval		5 years
Rottenstrasse 5 in Visp \| Maximum \| Switzerland \| Lease Agreement on April 2020
Commitments And Contingencies Disclosure [Line Items]
Lessee, Operating Lease, Term of Contract		15 years
Lessee, operating lease, term of contract		15 years
1200 Page Mill Road in Palo Alto \| California \| Lease Agreement on June 2020
Commitments And Contingencies Disclosure [Line Items]
Lessee operating lease option to extend	6.5
1250 Page Mill Road in Palo Alto \| California \| Lease Agreement on June 2020
Commitments And Contingencies Disclosure [Line Items]
Number of options to extend lease term \| Options	2
Initial lease term	13 years
Lessee operating lease option to extend	five