Derivative Instruments - Summary of Derivative Instruments (Details) - USD ($) $ in Thousands	3 Months Ended
Mar. 31, 2020	Mar. 31, 2019
Fair Value of Derivative Instruments
Realized (gain) loss on derivative instruments, net	$ (235)	$ (704)
Comprehensive loss \| Interest Rate Swap [Member] \| Designated as Hedging Instrument [Member]
Fair Value of Derivative Instruments
Designated derivative instruments	129,614
Gain (Loss) on Derivative Instruments [Member] \| Interest Rate Swap [Member] \| Not Designated as Hedging Instrument [Member]
Fair Value of Derivative Instruments
Realized (gain) loss on derivative instruments, net	(235)	(704)
Unrealized (Gain) Loss On Derivative Instruments [Member] \| Interest Rate Swap [Member] \| Not Designated as Hedging Instrument [Member]
Fair Value of Derivative Instruments
Non-designated derivative instruments	(297)	(986)
Interest and Debt Expense \| Interest Rate Swap [Member] \| Designated as Hedging Instrument [Member]
Fair Value of Derivative Instruments
Derivative Instruments, Gain (Loss) Reclassified from Accumulated OCI into Income, Effective Portion, Net	$ (1,259)	2,355
Comprehensive loss \| Interest Rate Swap [Member] \| Designated as Hedging Instrument [Member]
Fair Value of Derivative Instruments
Designated derivative instruments		$ 16,467

Derivative Instrument, Amortization of Interest Rate

No definition available.

Name:	trtn_DerivativeInstrumentAmortizationofInterestRate
Namespace Prefix:	trtn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The effective portion of net gain (loss) reclassified from accumulated other comprehensive income into income on derivative instruments designated and qualifying as hedging instruments.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4D
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=109980867&loc=SL5624177-113959

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4C
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=109980867&loc=SL5624171-113959

+ Details

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

- Definition

Amount of realized and unrealized gain (loss) of derivative instruments not designated or qualifying as hedging instruments.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4CC
-URI http://asc.fasb.org/extlink&oid=109980867&loc=SL109998890-113959

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4C
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=109980867&loc=SL5624171-113959

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

Amount before tax of increase (decrease) in accumulated gain (loss) from derivative instruments designated and qualifying as the effective portion of cash flow hedges and an entity's share of an equity investee's increase (decrease) in deferred hedging gain (loss).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 30
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=109978405&loc=d3e80720-113993

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 10A
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669646-108580

+ Details

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

- Details

Name:	us-gaap_OtherComprehensiveIncomeLocationAxis=us-gaap_OtherComprehensiveIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_GainLossOnDerivativeInstrumentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_NondesignatedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=trtn_UnrealizedGainLossOnDerivativeInstrumentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_InterestExpenseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_OtherComprehensiveIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: