Debt - Key Term and Carrying Value (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Debt Instrument [Line Items]
Debt outstanding	$ 6,613,118	$ 6,684,162
Deferred financing costs	34,088	39,781
Unamortized purchase price debt adjustments	3,514	4,065
Unamortized debt premiums & discounts	6,410	8,791
Debt, net of unamortized debt costs	$ 6,569,106	6,631,525
Institutional notes
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	4.59%
Debt outstanding	$ 1,733,671	1,957,557
Asset-backed securitization term notes
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	3.26%
Debt outstanding	$ 2,527,680	2,719,206
Term loan facilities
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	1.71%
Debt outstanding	$ 1,144,875	1,200,375
Asset-backed securitization warehouse
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	1.94%
Debt outstanding	$ 470,000	370,000
Revolving credit facilities
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	1.78%
Debt outstanding	$ 718,500	410,000
Capital lease obligations
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	4.93%
Debt outstanding	$ 18,392	27,024
Level 2
Debt Instrument [Line Items]
Debt outstanding	$ 6,683,500	$ 6,747,800

Adjustment to Purchase Price of Debt

No definition available.

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

- Definition

Debt and Capital Lease Obligations, net of deferred financing costs

+ References

No definition available.

+ Details

Name:	trtn_DebtandCapitalLeaseObligationsnetofdeferredfinancingcosts
Namespace Prefix:	trtn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of short-term and long-term debt and lease obligation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.13,16)
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03.16)
-URI http://asc.fasb.org/extlink&oid=119400593&loc=d3e572229-122910

+ Details

Name:	us-gaap_DebtAndCapitalLeaseObligations
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Effective interest rate for the funds borrowed under the debt agreement considering interest compounding and original issue discount or premium.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 6
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109500613&loc=SL6036836-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28551-108399

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateEffectivePercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

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

- Definition

Amount, after accumulated amortization, of debt discount (premium).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28555-108399

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28551-108399

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28567-108399

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 1A
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28541-108399

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

+ Details

Name:	us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, after accumulated amortization, of debt issuance costs. Includes, but is not limited to, legal, accounting, underwriting, printing, and registration costs.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.17)
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28555-108399

+ Details

Name:	us-gaap_DeferredFinanceCostsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=trtn_InstitutionalNotesDomain
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=trtn_AssetBackedSecuritizationTermNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=trtn_TermNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=trtn_AssetBackedWarehouseFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_LineOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_CapitalLeaseObligationsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: