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Stockholders' Equity (Schedule of Assumptions Used in Estimate of Fair Value of Stock Option Awards) (Details) - $ / shares
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted-average grant date market value of Woodward stock $ 78.91 $ 69.45 $ 40.26
Weighted-average exercise price per share 78.91 62.74 40.26
Minimum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted-average grant date market value of Woodward stock 78.91 69.45 40.26
Weighted-average exercise price per share $ 78.91 $ 62.74 $ 40.26
Expected term 6 years 4 months 24 days 6 years 6 years 3 months 18 days
Estimated volatility 29.10% 30.60% 34.50%
Estimated dividend yield 0.60% 0.70% 1.00%
Risk-free interest rate 2.10% 2.00% 1.70%
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 32.70% 33.70% 35.10%
Estimated dividend yield 0.80% 0.70% 1.00%
Risk-free interest rate 2.80% 2.50% 2.00%