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Income Taxes (Details) (USD $)
In Millions, unless otherwise specified
3 Months Ended 6 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Mar. 31, 2015
Mar. 31, 2014
Sep. 30, 2014
Income Tax Disclosure [Abstract]          
Effective income tax rate 25.50%us-gaap_EffectiveIncomeTaxRateContinuingOperations 27.40%us-gaap_EffectiveIncomeTaxRateContinuingOperations 25.50%us-gaap_EffectiveIncomeTaxRateContinuingOperations 27.40%us-gaap_EffectiveIncomeTaxRateContinuingOperations  
U.S. statutory rate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate  
Gross unrecognized tax benefits $ 40.5us-gaap_UnrecognizedTaxBenefits   $ 40.5us-gaap_UnrecognizedTaxBenefits   $ 38.9us-gaap_UnrecognizedTaxBenefits
Accrued interest and penalties related to unrecognized tax benefits 5.6us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued   5.6us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued   8.1us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued
Net reduction of income tax provision related to unrecognized tax benefits, tax penalties, accrued interest and offsetting tax assets 22.3rok_NetImpactonIncomeTaxProvisionofUnrecognizedTaxBenefitsTaxPenaltiesAccruedInterestandOffsettingTaxAssets   22.3rok_NetImpactonIncomeTaxProvisionofUnrecognizedTaxBenefitsTaxPenaltiesAccruedInterestandOffsettingTaxAssets    
Reasonably possible amount of decrease in gross unrecognized tax benefits for the next twelve months 20.5us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleAmountOfUnrecordedBenefit   20.5us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleAmountOfUnrecordedBenefit    
Reasonably possible amount of net reduction to income tax provision if unrecognized tax benefits were recognized $ 3.1rok_SignificantChangeinUnrecognizedTaxBenefitsisReasonablyPossibleEstimatedRangeofChangeUpperBoundNetImpactonTaxProvision   $ 3.1rok_SignificantChangeinUnrecognizedTaxBenefitsisReasonablyPossibleEstimatedRangeofChangeUpperBoundNetImpactonTaxProvision    
Earliest open year for income tax examinations, U.S. federal     2012    
Earliest open tax year for income tax examinations, state, local and non-U.S.     2003