Amount authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481520/505-30-50-4

+ Details

Name:	srt_StockRepurchaseProgramAuthorizedAmount1
Namespace Prefix:	srt_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Number of shares of common stock outstanding. Common stock represent the ownership interest in a corporation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.6-05(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(16)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(7))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

+ Details

Name:	us-gaap_CommonStockSharesOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Aggregate share number for all nonredeemable preferred stock (or preferred stock redeemable solely at the option of the issuer) held by stockholders. Does not include preferred shares that have been repurchased.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.6-05(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(16)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(7))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

+ Details

Name:	us-gaap_PreferredStockSharesOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number, before forfeiture, of shares issued under share-based payment arrangement. Excludes employee stock ownership plan (ESOP).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Equity impact of the value of stock that has been repurchased during the period and has not been retired and is not held in treasury. Some state laws may mandate the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 830
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479168/946-830-55-11

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 205
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478009/946-205-45-4

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 505
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478448/946-505-50-2

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

Reference 8: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

+ Details

Name:	us-gaap_StockRepurchasedDuringPeriodValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Number of previously issued common shares repurchased by the issuing entity and held in treasury.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 505
-SubTopic 30
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481549/505-30-45-1

+ Details

Name:	us-gaap_TreasuryStockCommonShares
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of shares that have been repurchased during the period and are being held in treasury.

+ References

+ Details

Name:	us-gaap_TreasuryStockSharesAcquired
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_PreferredStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ShareRepurchaseProgramAxis=tt_A2024AuthorizationDomain
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ShareRepurchaseProgramAxis=tt_A2022AuthorizationDomain
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CurrencyAxis=srt_OtherCurrencyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_TreasuryStockCommonMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Equity (Reconciliation of Ordinary Shares) (Details) - USD ($) $ in Millions	3 Months Ended						9 Months Ended
	Sep. 30, 2025	Jun. 30, 2025	Mar. 31, 2025	Sep. 30, 2024	Jun. 30, 2024	Mar. 31, 2024	Sep. 30, 2025	Dec. 31, 2024	Dec. 05, 2024	Feb. 28, 2022
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Treasury Stock, Common, Shares	24,500,000						24,500,000	24,500,000
Preferred Stock [Member]
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Preferred Stock, Shares Outstanding	0						0	0
2024 Authorization [Domain]
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock Repurchase Program, Authorized Amount									$ 5,000.0
2022 Authorization [Domain]
Stock Repurchased During Period, Value	$ 370.0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock Repurchase Program, Authorized Amount										$ 3,000.0
Other Currency \| Ordinary shares
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (shares)			0				0
Ending balance (shares)	0						0
Ordinary shares
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (shares)	247,200,000	248,000,000.0	249,000,000.0	250,400,000	251,200,000	251,700,000	249,000,000.0
Shares issued under incentive plans, net							800,000
Treasury Stock, Shares, Acquired	900,000	1,100,000	1,300,000	800,000	1,000,000.0	1,200,000	3,300,000
Ending balance (shares)	246,500,000	247,200,000	248,000,000.0	249,700,000	250,400,000	251,200,000	246,500,000
Treasury Stock, Common
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Shares issued under incentive plans, net							0
Treasury Stock, Shares, Acquired							0