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Other Non-current Assets - Investments in Joint Ventures (Details) $ in Millions	1 Months Ended			3 Months Ended	12 Months Ended
	Sep. 30, 2022 USD ($)	Jun. 30, 2020 USD ($)	Jun. 30, 2011	May 31, 2022 USD ($) engine	May 31, 2024 USD ($)	May 31, 2023 USD ($)	May 31, 2022 USD ($)
Investments in Joint Ventures
Investments in joint ventures					$ 35.8	$ 16.6
Income (losses) from joint ventures					(0.2)	(3.2)	$ (2.9)
License Fees
License fees, net					51.8	39.6
AAR sumisho aviation services
Investments in Joint Ventures
Income (losses) from joint ventures					4.9	1.5	1.0
Unison Industries
License Fees
Agreement period (in years)	1 year		10 years
Payment of license fee	$ 18.0	$ 25.0
License fee capitalized	$ 18.0	$ 25.0
License fees, net					$ 33.0
Owned Through Joint Ventures
Investments in Joint Ventures
Percentage on outstanding debt					40.00%
Owned Through Joint Ventures \| Aircraft
Investments in Joint Ventures
Payment of evaluation and inspection services					$ 1.6	1.0	1.1
Number of aircraft engines acquired \| engine				2
Payments to acquire aircraft and engine				$ 16.8			16.8
Remarketing fees earned				0.2
Net cash proceeds from sale of aircraft by joint ventures				$ 17.0
Owned Through Joint Ventures \| Joint venture in India to operate an airframe maintenance facility
Investments in Joint Ventures
Investments in joint ventures					$ 10.1
Ownership interest in joint ventures (as a percent)					40.00%
Owned Through Joint Ventures \| Joint venture in India
Investments in Joint Ventures
Investments in joint ventures					$ 6.5
Percentage on outstanding debt					40.00%
Amount of guarantee liability recognized					$ 9.4
Loan to joint venture					3.6
Income (losses) from joint ventures					$ 0.2	$ (2.7)	$ (1.8)
Owned Through Joint Ventures \| AAR sumisho aviation services
Investments in Joint Ventures
Ownership interest in joint ventures (as a percent)					50.00%