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Stockholders' Equity (Schedule of Assumptions Used in Estimate of Fair Value of Stock Option Awards) (Details) - Stock Options [Member] - $ / shares
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted-average exercise price per share $ 79.84 $ 78.91 $ 62.74
Weighted-average grant date market value of Woodward stock $ 79.84 $ 78.91 $ 69.45
Estimated dividend yield     0.70%
Minimum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected term 6 years 6 months 6 years 4 months 24 days 6 years
Estimated volatility 25.70% 29.10% 30.60%
Estimated dividend yield 0.60% 0.60%  
Risk-free interest rate 1.50% 2.10% 2.00%
Maximum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected term 8 years 8 months 12 days 8 years 8 months 12 days 8 years 8 months 12 days
Estimated volatility 31.00% 32.70% 33.70%
Estimated dividend yield 0.80% 0.80%  
Risk-free interest rate 3.10% 2.80% 2.50%