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Income Taxes - Narrative (Details) - USD ($)	12 Months Ended
Income Taxes - Narrative (Details) - USD ($)	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Income Tax Contingency [Line Items]
Undistributed earnings and original investments in foreign subsidiaries		$ 305,500,000
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes		400,000
Unrecognized tax benefits		21,100,000	$ 20,100,000	$ 19,500,000	$ 17,700,000
Unrecognized tax benefits that if recognized would affect annual effective tax rate		21,100,000	20,100,000
Anticipated decrease in unrecognized tax benefits within the next twelve months		11,800,000
Reductions due to lapse of statute of limitations		3,100,000	2,900,000	1,600,000
Total accrued interest		4,600,000	$ 3,300,000	$ 2,100,000
Accruals related to income tax penalties		0
Forecast
Income Tax Contingency [Line Items]
Reductions due to lapse of statute of limitations	$ 3,500,000
Internal Revenue Service (IRS)
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration		10,500,000
Tax credit carryforward subject to a full valuation allowance		9,700,000
Operating loss carryforwards		10,500,000
State and Local Jurisdiction
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration		900,000
Operating loss carryforwards		28,800,000
Foreign Tax Jurisdiction
Income Tax Contingency [Line Items]
Operating loss carryforwards		$ 14,600,000