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Stockholders' Equity (Schedule of Assumptions Used in Estimate of Fair Value of Stock Option Awards) (Details) - Stock Options [Member] - $ / shares
3 Months Ended 9 Months Ended
Jun. 30, 2020
Jun. 30, 2020
Jun. 30, 2019
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Weighted-average exercise price per share $ 58.40 $ 90.57 $ 79.12
Weighted-average grant date market value of Woodward stock $ 58.40 $ 90.57 $ 79.12
Expected term (years) 6 years 6 months    
Risk-free interest rate 0.40%    
Minimum [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Expected term (years)   6 years 4 months 24 days 6 years 6 months
Estimated volatility 33.10% 25.70% 25.70%
Estimated dividend yield 0.50% 0.50% 0.70%
Risk-free interest rate   0.40% 2.60%
Maximum [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Expected term (years)   8 years 8 months 12 days 8 years 8 months 12 days
Estimated volatility 34.30% 34.30% 31.00%
Estimated dividend yield 0.60% 0.90% 0.80%
Risk-free interest rate   1.70% 3.10%