Earnings per Share (Details) (USD $) In Millions, except Share data, unless otherwise specified	3 Months Ended	6 Months Ended
Nov. 30, 2014	Nov. 30, 2013	Nov. 30, 2014	Nov. 30, 2013
Earnings per Share
Effect to the participating securities as result of net loss			$ 0
Basic EPS:
Net income attributable to AAR and noncontrolling interest	15.2us-gaap_ProfitLoss	20.0us-gaap_ProfitLoss	29.7us-gaap_ProfitLoss	38.0us-gaap_ProfitLoss
Less income attributable to participating shares	(0.3)	(0.4)	(0.6)	(0.8)
Less income attributable to noncontrolling interest			(0.1)	(0.1)
Net income attributable to AAR available to common shareholders	14.9	19.6	29.0	37.1
Basic shares:
Weighted average common shares outstanding	38,700,000	38,600,000	38,700,000	38,600,000
Earnings per share - basic:
Earnings per share - basic (in dollars per share)	$ 0.38us-gaap_EarningsPerShareBasic	$ 0.51us-gaap_EarningsPerShareBasic	$ 0.75us-gaap_EarningsPerShareBasic	$ 0.96us-gaap_EarningsPerShareBasic
Diluted EPS:
Net income attributable to AAR and noncontrolling interest	15.2us-gaap_ProfitLoss	20.0us-gaap_ProfitLoss	29.7us-gaap_ProfitLoss	38.0us-gaap_ProfitLoss
Less income attributable to participating shares	(0.3)	(0.4)	(0.6)	(0.8)
Less income attributable to noncontrolling interest			(0.1)	(0.1)
Net income attributable to AAR available to common shareholders	$ 14.9	$ 19.6	$ 29.0	$ 37.1
Diluted shares:
Weighted average common shares outstanding	38,700,000	38,600,000	38,700,000	38,600,000
Additional shares from the assumed exercise of stock options	400,000	600,000	500,000	500,000
Weighted average common shares outstanding - diluted	39,100,000	39,200,000	39,200,000	39,100,000
Earnings per share - diluted:
Earnings per share - diluted (in dollars per share)	$ 0.38us-gaap_EarningsPerShareDiluted	$ 0.50us-gaap_EarningsPerShareDiluted	$ 0.74us-gaap_EarningsPerShareDiluted	$ 0.95us-gaap_EarningsPerShareDiluted
Antidilutive stock options excluded from the computation of diluted earnings per share (in shares)			185,163	48,000

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The value of the aggregate of earnings distributed and earnings allocated to participating securities under the two-class method for purposes of the basic earnings per share calculation to the extent that participating securities may share in earnings as if all of the earnings for the period had been distributed.

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The amount of net income (loss) for the period per each share of common stock or unit outstanding during the reporting period.

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The amount of net income (loss) for the period available to each share of common stock or common unit outstanding during the reporting period and to each share or unit that would have been outstanding assuming the issuance of common shares or units for all dilutive potential common shares or units outstanding during the reporting period.

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Amount of Net Income (Loss) attributable to noncontrolling interest.

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Net income after adjustments for dividends on preferred stock (declared in the period) and/or cumulative preferred stock (accumulated for the period).

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Net Income or Loss Available to Common Stockholders plus adjustments resulting from the assumption that dilutive convertible securities were converted, options or warrants were exercised, or that other shares were issued upon the satisfaction of certain conditions.

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The consolidated profit or loss for the period, net of income taxes, including the portion attributable to the noncontrolling interest.

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