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Share-based Payments - Narrative (Details) - USD ($) | 12 Months Ended |  |  |
--- | --- | --- | --- | ---
Aug. 31, 2024 | Aug. 31, 2023 | Aug. 31, 2022 | Jan. 31, 2022 | Dec. 31, 2021 | Aug. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment expense | $ 46,600,000 | $ 42,000,000.0 | $ 37,400,000 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares authorized for issuance (in shares) |  |  |  | 3,600,000 | 2,700,000 |
Number of shares available for grant (in shares) | 700,000 | 1,000,000.0 | 1,100,000 |  |  |
Stock options outstanding (in shares) | 900,000 | 1,000,000.0 | 1,100,000 |  |  | 1,200,000
Share-based payment expense | $ 46,600,000 | $ 42,000,000.0 | $ 37,400,000 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares outstanding of restricted stock (in shares) | 300,000 | 300,000 | 300,000 |  |  | 400,000
Unrecognized compensation cost | $ 30,100,000 |  |  |  |  |
Unrecognized compensation cost period of recognition (years) | 1 year 3 months 18 days |  |  |  |  |
Fair value of shares vested | $ 22,900,000 | $ 19,900,000 | $ 16,400,000 |  |  |
Awards that vested in the period (in shares) | 200,000 | 100,000 | 100,000 |  |  |
Share-based payment expense | $ 23,900,000 | $ 19,600,000 | $ 17,200,000 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units | Grants awarded beginning 2022 |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Share-based compensation vesting period (years) | 3 years |  |  |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted stock awards and units | Grants awarded prior to 2022 |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Share-based compensation vesting period (years) | 4 years |  |  |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Stock options |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Unrecognized compensation cost | $ 700,000 |  |  |  |  |
Stock options outstanding (in shares) | 900,000 |  |  |  |  |
Award expiration term | 10 years |  |  |  |  |
Intrinsic value of options exercised | $ 6,600,000 | 500,000 | 14,000,000 |  |  |
Total intrinsic value of stock options outstanding | 116,500,000 |  |  |  |  |
Total intrinsic value of stock options expected to vest | 10,100,000 |  |  |  |  |
Total intrinsic value of stock options exercisable | 106,400,000 |  |  |  |  |
Share-based payment expense | $ 2,600,000 | $ 5,700,000 | $ 8,800,000 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Stock options | Market Options |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Share-based compensation vesting period (years) | 4 years |  |  |  |  |
Stock options outstanding (in shares) | 300,000 |  |  |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Performance stock units |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares outstanding of restricted stock (in shares) | 300,000 | 200,000 | 200,000 |  |  | 200,000
Share-based compensation vesting period (years) | 3 years | 3 years |  |  |  |
Unrecognized compensation cost | $ 12,600,000 |  |  |  |  |
Unrecognized compensation cost period of recognition (years) | 1 year 4 months 24 days |  |  |  |  |
Fair value of shares vested | $ 5,000,000.0 | $ 11,500,000 | $ 0 |  |  |
Awards that vested in the period (in shares) | 100,000 | 100,000 |  |  |  |
Performance stock units outstanding | 300,000 |  |  |  |  |
Share-based payment expense | $ 18,600,000 | $ 15,200,000 | 9,900,000 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Employee Deferred Stock Units |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares vested (in shares) | 4,000 |  |  |  |  |
Share-based payment expense | $ 0 | $ 0 | $ 0 |  |  |
Omnibus Stock Compensation Incentive and Directors’ Equity Plans | Restricted Stock Units (RSUs) |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares vested (in shares) | 38,000 |  |  |  |  |
Employee Stock Purchase Plan |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares authorized for issuance (in shares) | 1,500,000 |  |  |  |  |
Number of shares available for grant (in shares) | 1,000,000.0 |  |  |  |  |
Employee discount on purchases of common stock | 5.00% |  |  |  |  |

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