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Share-based Payments - Share-based Compensation Expense Recognized (Details) - USD ($) $ in Millions | 12 Months Ended
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Aug. 31, 2021 | Aug. 31, 2020 | Aug. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | $ 32.5 | $ 38.2 | $ 29.2
Stock Incentive Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | 32.5 | 38.2 | 29.2
Restricted stock awards and units | Stock Incentive Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | 15.1 | 24.6 | 25.1
Stock options | Stock Incentive Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | 9.2 | 4.9 | 2.7
Performance stock units | Stock Incentive Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | 6.8 | 7.3 | 0.0
Director stock units | Stock Incentive Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based payment expense | $ 1.4 | $ 1.4 | $ 1.4

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