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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
Dec. 31, 2018
Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Weighted-average exercise price per share $ 79.79 $ 78.97
Weighted-average grant date market value of Woodward stock $ 79.79 $ 78.97
Expected term   6 years 4 months 24 days
Estimated dividend yield   0.60%
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
Estimated volatility 25.70% 30.30%
Estimated dividend yield 0.70%  
Risk-free interest rate 2.70% 2.10%
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 31.00% 32.70%
Estimated dividend yield 0.80%  
Risk-free interest rate 3.10% 2.30%