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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 6 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Mar. 31, 2020
Mar. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Weighted-average exercise price per share $ 127.84 $ 77.12 $ 104.91 $ 79.12
Weighted-average grant date market value of Woodward stock $ 127.84 $ 77.12 $ 104.91 $ 79.12
Expected term 6 years 6 months 6 years 6 months    
Estimated volatility 25.70%      
Estimated dividend yield 0.90%      
Risk-free interest rate 1.70% 2.60%    
Minimum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Expected term     6 years 4 months 24 days 6 years 6 months
Estimated volatility   25.80% 25.70% 25.70%
Estimated dividend yield   0.70% 0.60% 0.70%
Risk-free interest rate     1.60% 2.60%
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
Estimated volatility   26.00% 30.10% 31.00%
Estimated dividend yield   0.80% 0.90% 0.80%
Risk-free interest rate     1.70% 3.10%