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Income Taxes - Narrative (Details) - USD ($)	Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018
Income Tax Contingency [Line Items]
Undistributed earnings and original investments in foreign subsidiaries	$ 165,100,000
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes	3,300,000
State tax credit carryforwards	1,500,000
Unrecognized tax benefits	17,700,000	$ 17,200,000	$ 16,600,000	$ 4,400,000
Unrecognized tax benefits that if recognized would affect annual effective tax rate	17,100,000	16,700,000
Total accrued interest	2,000,000	$ 1,700,000	$ 1,000,000
Accruals related to income tax penalties	0
Internal Revenue Service (IRS)
Income Tax Contingency [Line Items]
Operating loss carryforwards	28,700,000
State and Local Jurisdiction
Income Tax Contingency [Line Items]
Operating loss carryforwards	30,100,000
Foreign Tax Authority
Income Tax Contingency [Line Items]
Operating loss carryforwards	$ 3,400,000