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Income Taxes - Reconciliation of U.S. Federal Statutory Tax Rate to Effective Tax Rate (Details)
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Operating Loss Carryforwards [Line Items]      
U.S. federal statutory tax rate 21.00% 21.00% 21.00%
Difference in tax rate due to:      
State, net of federal benefit 1.50% 1.90% 2.80%
Valuation allowance adjustments (0.50%) 1.00% 0.00%
Effects of foreign operations 4.40% 4.60% 1.30%
Excess tax benefits on share-based payments (0.30%) (0.10%) (0.20%)
Other, net 0.20% (0.10%) (0.30%)
Effective tax rate 22.60% 26.20% 20.20%
Effects of U.S. tax legislation      
Difference in tax rate due to:      
Effect of tax rate change 0.00% (0.80%) (4.70%)
Effects of tax rate changes - International      
Difference in tax rate due to:      
Effect of tax rate change (2.30%) (1.30%) 0.30%
Effects of tax rate changes – State, net of federal benefit      
Difference in tax rate due to:      
Effect of tax rate change (1.40%) 0.00% 0.00%