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Stockholders' Equity (Schedule of Assumptions Used in Estimate of Fair Value of Stock Option Awards) (Details) - Stock Options [Member] - $ / shares
9 Months Ended
Jun. 30, 2019
Jun. 30, 2018
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
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
Estimated volatility 25.70% 29.10%
Estimated dividend yield 0.70% 0.60%
Risk-free interest rate 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
Estimated volatility 31.00% 32.70%
Estimated dividend yield 0.80% 0.80%
Risk-free interest rate 3.10% 2.80%