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Share-based Payments - Narrative (Details) - USD ($)	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021	Jan. 31, 2022	Dec. 31, 2021	Aug. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	$ 42,000,000	$ 37,400,000	$ 32,500,000
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)	1,000,000	1,100,000	300,000
Share-based payment expense	$ 42,000,000.0	$ 37,400,000	$ 32,500,000
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	400,000			400,000
Unrecognized compensation cost	$ 31,800,000
Unrecognized compensation cost period of recognition (years)	1 year 3 months 18 days
Fair value of shares vested	$ 19,900,000	$ 16,400,000	$ 19,500,000
Awards that vested in the period (in shares)	100,000	100,000	100,000
Share-based payment expense	$ 19,600,000	$ 17,200,000	$ 15,100,000
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 | 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 | Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost	$ 3,200,000
Unrecognized compensation cost period of recognition (years)	1 year 2 months 12 days
Stock options outstanding (in shares)	1,000,000.0	1,100,000	1,200,000			900,000
Award expiration term	10 years
Intrinsic value of options exercised	$ 500,000	$ 14,000,000	$ 1,200,000
Total intrinsic value of stock options outstanding	37,900,000
Total intrinsic value of stock options expected to vest	8,300,000
Total intrinsic value of stock options exercisable	29,600,000
Share-based payment expense	$ 5,700,000	$ 8,800,000	$ 9,200,000
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)	200,000	200,000	200,000			100,000
Share-based compensation vesting period (years)	3 years
Unrecognized compensation cost	$ 11,700,000
Unrecognized compensation cost period of recognition (years)	1 year 4 months 24 days
Fair value of shares vested	$ 11,500,000
Awards that vested in the period (in shares)	100,000	0	0
Performance stock units outstanding	200,000
Share-based payment expense	$ 15,200,000	$ 9,900,000	$ 6,800,000
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)	45,000
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
Employee discount on purchases of common stock	5.00%

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Period from grant date that an equity-based award expires, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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- Definition

Amount of difference between fair value of the underlying shares reserved for issuance and exercise price of vested portions of options outstanding and currently exercisable.

+ References

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