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Income Taxes - Narrative (Details) - USD ($) | Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020 | Aug. 31, 2019
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Income Tax Contingency [Line Items] |  |  |  |
Undistributed earnings and original investments in foreign subsidiaries | $ 204,000,000 |  |  |
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes | 3,200,000 |  |  |
Unrecognized tax benefits | 19,500,000 | $ 17,700,000 | $ 17,200,000 | $ 16,600,000
Unrecognized tax benefits that if recognized would affect annual effective tax rate | 18,800,000 | 17,100,000 |  |
Total accrued interest | 2,100,000 | $ 2,000,000 | $ 1,700,000 |
Accruals related to income tax penalties | 0 |  |  |
Internal Revenue Service (IRS) |  |  |  |
Income Tax Contingency [Line Items] |  |  |  |
Federal tax credit carryforwards, subject to expiration | 4,900,000 |  |  |
Operating loss carryforwards | 13,600,000 |  |  |
State and Local Jurisdiction |  |  |  |
Income Tax Contingency [Line Items] |  |  |  |
Federal tax credit carryforwards, subject to expiration | 100,000 |  |  |
Operating loss carryforwards | 33,900,000 |  |  |
Foreign Tax Authority |  |  |  |
Income Tax Contingency [Line Items] |  |  |  |
Operating loss carryforwards | $ 7,100,000 |  |  |

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