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Stock Based Compensation (Details) (USD $)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Stock Based Compensation [Abstract]    
Percentage of eligible earnings to purchase common stock through the employee stock purchase plan (in hundredths) 10.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate  
Discount on the average closing price for the employee stock purchase plan (in hundredths) 5.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardDiscountFromMarketPricePurchaseDate  
Stock Based Compensation Expense [Abstract]    
Stock based compensation $ 13,801,000us-gaap_AllocatedShareBasedCompensationExpense $ 14,571,000us-gaap_AllocatedShareBasedCompensationExpense
Tax effect recognized in net income 4,830,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense 5,100,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
Windfall tax benefit/(shortfall), net 4,107,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions 7,485,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions
Employee stock options granted during the period (in shares) 537,555us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod 533,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod
Fair value per share (in dollars per share) $ 33.76us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 35.14us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Weighted average assumptions used to value option grants [Abstract]    
Risk-free interest rate (%) (in hundredths) 1.51%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate 1.62%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Expected option life (years) 5 years 1 month 6 days 5 years 2 months 26 days
Expected volatility (%) (in hundredths) 22.28%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate 27.62%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
Expected dividend yield (%) (in hundredths) 0.63%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate 0.59%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
Cash received from exercise of options 7,400,000us-gaap_ProceedsFromStockOptionsExercised 10,000,000us-gaap_ProceedsFromStockOptionsExercised
Restricted stock awards granted during period (in shares) 304,175rop_ShareBasedCompensationArrangementByShareBasedPaymentAwardRestrictedGrantsInPeriod 237,001rop_ShareBasedCompensationArrangementByShareBasedPaymentAwardRestrictedGrantsInPeriod
Weighted average fair value per share of restricted stock awards granted during the period (in dollars per share) $ 149.66us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 139.62us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Restricted stock awards vested during period (in shares) 26,686us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod  
Weighted average grant date fair value per share (in dollars per share) $ 124.27us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue  
Weighted average vest date fair value per share (in dollars per share) $ 157.59rop_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageVestDateFairValue  
Shares of stock purchased during the period by participants in the employee stock purchase plan (in shares) 5,042us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans 5,664us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans
Amount paid for stock purchased during the period by participants in the employee stock purchase plan $ 790,000rop_StockPurchasedDuringPeriodValueEmployeeStockPurchasePlans $ 730,000rop_StockPurchasedDuringPeriodValueEmployeeStockPurchasePlans