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Income Taxes - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
Income Taxes - Narrative (Details) - USD ($) $ in Millions	Aug. 31, 2026	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Income Tax Contingency [Line Items]
Undistributed earnings and original investments in foreign subsidiaries		$ 365.4
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes		0.4
Unrecognized tax benefits		18.5	$ 21.1	$ 20.1	$ 19.5
Unrecognized tax benefits that if recognized would affect annual effective tax rate		18.5	21.1
Anticipated decrease in unrecognized tax benefits within the next twelve months		5.6
Reductions due to lapse of statute of limitations		8.3	3.1	2.9
Total accrued interest		2.4	$ 4.6	$ 3.3
Accruals related to income tax penalties		0.8
Forecast
Income Tax Contingency [Line Items]
Reductions due to lapse of statute of limitations	$ 1.3
Internal Revenue Service (IRS)
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration		11.2
Tax credit carryforward subject to a full valuation allowance		9.1
State and Local Jurisdiction
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration		0.5
Operating loss carryforwards		27.4
Foreign Tax Jurisdiction
Income Tax Contingency [Line Items]
Operating loss carryforwards		$ 15.2