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Derivative Instruments - Interest Rate Swap/Caps (Details) $ in Millions	12 Months Ended
	Dec. 31, 2023 USD ($)
Interest Rate Swap [Member]
Fair Value of Derivative Instruments
Weighted Average Fixed Leg (Pay) Interest Rate	2.63%
Weighted Average Remaining Term	3 years 8 months 12 days
Designated as Hedging Instrument [Member] | Interest Rate Swap [Member]
Fair Value of Derivative Instruments
Notional Amount (in millions)	$ 1,847.0
Designated as Hedging Instrument [Member] | Forward Contracts [Member]
Fair Value of Derivative Instruments
Weighted Average Remaining Term	4 years 7 months 6 days
Total Notional Amount Forward Starting Interest Rate Swap	$ 350.0

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- Definition

Weighted average remaining period until maturity of net outstanding interest rate swap agreements, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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No definition available.

+ Details

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Namespace Prefix:	trtn_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

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- Definition

The net notional amount of interest rate swap/cap agreements, which relate to the currency amounts specified in the related agreement.

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No definition available.

+ Details

Name:	trtn_NetNotionalAmountofInterestRateAgreements
Namespace Prefix:	trtn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

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- Definition

Net Notional Amount of Interest Rate During Period

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No definition available.

+ Details

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Namespace Prefix:	trtn_
Data Type:	dtr-types1:percentItemType
Balance Type:	na
Period Type:	duration

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- Definition

Total Notional Amount Forward Starting Interest Rate Swap

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No definition available.

+ Details

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Namespace Prefix:	trtn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

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- 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.

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No definition available.

+ Details

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

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- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_InterestRateSwapMember
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Balance Type:
Period Type:

X

- Details

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

X

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForwardContractsMember
Namespace Prefix:
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Balance Type:
Period Type: