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Stock-based Compensation - Narrative (Details) - USD ($)	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2021
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Number of shares available for grant	973,514
Share-based arrangement, tax benefit	$ 1,700,000	$ 1,400,000	$ 1,300,000
Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)	18,522
Share-based arrangement, tax benefit	$ 1,500,000	$ 1,300,000	$ 800,000
Compensation cost not yet recognized	$ 1,700,000
Remaining weighted-average vesting periods	1 year 6 months 29 days
Weighted-average grant date fair value (in dollars per share)	$ 253.47	$ 206.85	$ 167.05
Intrinsic value of shares converted	$ 6,300,000	$ 6,700,000	$ 3,700,000
Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)	14,233
Share-based arrangement, tax benefit	$ 700,000
Compensation cost not yet recognized	$ 4,200,000
Remaining weighted-average vesting periods	1 year 10 months 2 days
Weighted-average grant date fair value (in dollars per share)	$ 281.09	$ 226.30	$ 184.15
Intrinsic value of shares converted	$ 3,100,000	$ 0	$ 0
Expected dividend yield	0.00%	0.00%	0.00%
Deferred Performance Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)				0
Compensation cost not yet recognized	$ 0
Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)	16,978
Period of separation from service				6 months
Share-based arrangement, tax benefit	$ 200,000
Compensation cost not yet recognized	$ 0
Weighted-average grant date fair value (in dollars per share)	$ 251.30	$ 198.94	$ 170.16
Intrinsic value of shares converted	$ 800,000	$ 0	$ 0
Nonemployee directors \| Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	1 year
High Level Employees \| Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	3 years
High Level Employees \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	3 years
Minimum \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	0.00%
Minimum \| Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	0.00%
Maximum \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	200.00%
Maximum \| Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	100.00%