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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, 2019
Mar. 31, 2018
Mar. 31, 2019
Mar. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Weighted-average exercise price per share $ 77.12 $ 72.01 $ 79.12 $ 78.91
Weighted-average grant date market value of Woodward stock $ 77.12 $ 72.01 79.12 78.91
Expected term 6 years 6 months 6 years 4 months 24 days    
Estimated volatility   29.10%    
Estimated dividend yield   0.80%    
Risk-free interest rate 2.60%      
Minimum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Weighted-average exercise price per share     79.12 78.91
Weighted-average grant date market value of Woodward stock     $ 79.12 $ 78.91
Expected term 6 years 6 months 6 years 4 months 24 days 6 years 6 months 6 years 4 months 24 days
Estimated volatility 25.80% 29.10% 25.70% 29.10%
Estimated dividend yield 0.70%   0.70% 0.60%
Risk-free interest rate 2.60% 2.70% 2.60% 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 26.00%   31.00% 32.70%
Estimated dividend yield 0.80%   0.80% 0.80%
Risk-free interest rate   2.80% 3.10% 2.80%