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Stock-Based Compensation (Details) (USD $)
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Percentage of eligible earnings to purchase common stock through the employee stock purchase plan (in hundredths) 10.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate    
Discount rate to the average closing price at which employees may purchase stock (in hundredths) 5.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardDiscountFromMarketPriceOfferingDate    
Stock based compensation expense $ 63,000,000us-gaap_AllocatedShareBasedCompensationExpense $ 53,400,000us-gaap_AllocatedShareBasedCompensationExpense $ 40,800,000us-gaap_AllocatedShareBasedCompensationExpense
Tax effect recognized in net income 22,100,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense 18,700,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense 14,300,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
Windfall tax benefit, net 21,500,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions 16,000,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions 30,800,000us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions
Weighted average assumptions used in calculating the weighted average fair value of options granted      
Weighted average fair value of options granted (per share) $ 34.95us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 37.08us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 30.25us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Risk-free interest rate (%) (in hundredths) 1.63%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate 0.86%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate 0.77%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Average expected option life (in years) 5 years 2 months 19 days 5 years 2 months 8 days 5 years 2 months 26 days
Expected volatility (%) (in hundredths) 27.01%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate 36.09%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate 36.51%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
Expected dividend yield (%) (in hundredths) 0.58%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate 0.56%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate 0.58%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]      
Number of shares outstanding, beginning balance (in shares) 2,988,436us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 2,918,195us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber  
Number of shares granted (in shares) 650,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod 601,350us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod  
Options Exercised (in shares) (587,661)rop_StockIssuedDuringPeriodSharesStockOptionsExercisedWholeShares (424,945)rop_StockIssuedDuringPeriodSharesStockOptionsExercisedWholeShares  
Number of shares canceled (in shares) (69,664)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod (106,164)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod  
Number of shares outstanding, ending balance (in shares) 2,981,111us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 2,988,436us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 2,918,195us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Number of shares, options, exercisable, number (in shares) 1,811,238us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber    
Weighted Average Exercise Price [Abstract]      
Weighted average exercise price per share outstanding, beginning balance (in dollars per share) $ 74.00us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 63.15us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice  
Weighted average exercise price per share granted (in dollars per share) $ 137.05us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice $ 117.78us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice  
Weighted average exercise price per share exercised (in dollars per share) $ 55.98us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice $ 56.48us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice  
Weighted average exercise price per share cancelled (in dollars per share) $ 116.29us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice $ 98.74us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice  
Weighted average exercise price per share outstanding, ending balance (in dollars per share) $ 90.48us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 74.00us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice $ 63.15us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Weighted average remaining contractual term of options outstanding (in years) 6 years 4 months 13 days 6 years 2 months 19 days  
Aggregate intrinsic value of options outstanding 196,378,239us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue 193,279,214us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue  
Options, Exercisable, Weighted Average Exercise Price (in dollars per share) $ 68.02us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice    
Options, Exercisable, Weighted Average Remaining Contractual Term (in years) 4 years 10 months 28 days    
Options, Exercisable, Aggregate intrinsic value 159,978,254us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1    
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Total unrecognized compensation expense related to nonvested restricted stock granted to both employees and directors 27,600,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions    
Weighted-average period over which unrecognized compensation costs on non-vested stock options are expected to be recognized (in years) 1 year 10 months 24 days    
Intrinsic value of options exercised 50,300,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue 28,800,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue 86,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
Cash received from option exercises under all plans 32,500,000us-gaap_EmployeeServiceShareBasedCompensationCashReceivedFromExerciseOfStockOptions 24,000,000us-gaap_EmployeeServiceShareBasedCompensationCashReceivedFromExerciseOfStockOptions  
Summary of nonvested shares activity [Rollforward]      
Non-vested shares outstanding, beginning of period (in shares) 573,850us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber 571,905us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber  
Nonvested shares granted (in shares) 375,060us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod 399,540us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod  
Nonvested shares vested (in shares) (378,994)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod (373,946)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod  
Nonvested shares forfeited (in shares) (27,361)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod (23,649)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod  
Nonvested shares outstanding, end of period (in shares) 542,555us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber 573,850us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber 571,905us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
Restricted Stock Awards [Abstract]      
Weighted average fair value of nonvested shares, beginning of period (in dollars per share) $ 103.44us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue $ 80.96us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue  
Weighted Average Restricted Award Grant Date Fair Value (in dollars per share) $ 142.30us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 117.74us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue  
Weighted average fair value of shares vested (in dollars per share) $ 153.16us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue $ 126.80us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue  
Weighted average fair value of nonvested shares forfeited (in dollars per share) $ 106.60us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue $ 124.48us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue  
Weighted average fair value of nonvested shares, end of period (in dollars per share) $ 130.29us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue $ 103.44us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue $ 80.96us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
Total unrecognized compensation expense related to nonvested restricted stock granted to both employees and directors 43,400,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions    
Restricted Awards Outstanding, Weighted Average Remaining Contractual Terms 2 years 2 months 12 days    
Employee Stock Purchase Plan      
Shares of stock purchased during the period by participants in the employee stock purchase plan (in shares) 20,368us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans 20,211us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans 22,863us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans
Amount paid for stock purchased during the period by participants in the employee stock purchase plan 2,800,000us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlans 2,400,000us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlans 2,200,000us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlans
Employee Stock Ownership Plan (ESOP), Compensation Expense 0us-gaap_EmployeeStockOwnershipPlanESOPCompensationExpense 0us-gaap_EmployeeStockOwnershipPlanESOPCompensationExpense 0us-gaap_EmployeeStockOwnershipPlanESOPCompensationExpense
Exercise Price Range 1 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 31.66us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Exercise price range, upper range limit (in dollars per share) $ 47.49us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Options outstanding (in shares) 110,598us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Average exercise price of options outstanding (in dollars per share) $ 41.82us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Average remaining life of options outstanding (in years) 4 years 2 months 12 days    
Exercisable options (in shares) 110,598us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Average exercise price of exercisable options (in dollars per share) $ 41.82us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange1Member
   
Exercise Price Range 2 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 47.50us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Exercise price range, upper range limit (in dollars per share) $ 63.32us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Options outstanding (in shares) 911,913us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Average exercise price of options outstanding (in dollars per share) $ 54.10us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Average remaining life of options outstanding (in years) 3 years 3 months 18 days    
Exercisable options (in shares) 911,913us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Average exercise price of exercisable options (in dollars per share) $ 54.10us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange2Member
   
Exercise Price Range 3 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 63.33us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Exercise price range, upper range limit (in dollars per share) $ 79.15us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Options outstanding (in shares) 379,830us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Average exercise price of options outstanding (in dollars per share) $ 72.62us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Average remaining life of options outstanding (in years) 6 years 1 month 6 days    
Exercisable options (in shares) 379,830us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Average exercise price of exercisable options (in dollars per share) $ 72.62us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange3Member
   
Exercise Price Range 4 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 79.16us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Exercise price range, upper range limit (in dollars per share) $ 94.98us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Options outstanding (in shares) 325,632us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Average exercise price of options outstanding (in dollars per share) $ 92.70us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Average remaining life of options outstanding (in years) 7 years    
Exercisable options (in shares) 216,610us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Average exercise price of exercisable options (in dollars per share) $ 92.24us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange4Member
   
Exercise Price Range 5 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 94.99us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Exercise price range, upper range limit (in dollars per share) $ 110.81us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Options outstanding (in shares) 89,049us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Average exercise price of options outstanding (in dollars per share) $ 97.99us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Average remaining life of options outstanding (in years) 7 years 6 months    
Exercisable options (in shares) 51,717us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Average exercise price of exercisable options (in dollars per share) $ 98.07us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange5Member
   
Exercise Price Range 6 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 110.82us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Exercise price range, upper range limit (in dollars per share) $ 126.64us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Options outstanding (in shares) 512,589us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Average exercise price of options outstanding (in dollars per share) $ 117.12us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Average remaining life of options outstanding (in years) 8 years 2 months 12 days    
Exercisable options (in shares) 124,727us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Average exercise price of exercisable options (in dollars per share) $ 116.27us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange6Member
   
Exercise Price Range 7 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 126.65us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Exercise price range, upper range limit (in dollars per share) $ 142.47us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Options outstanding (in shares) 573,000us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Average exercise price of options outstanding (in dollars per share) $ 135.14us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Average remaining life of options outstanding (in years) 9 years 2 months 12 days    
Exercisable options (in shares) 15,843us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Average exercise price of exercisable options (in dollars per share) $ 133.77us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange7Member
   
Exercise Price Range 8 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 142.48us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Exercise price range, upper range limit (in dollars per share) $ 158.30us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Options outstanding (in shares) 78,500us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Average exercise price of options outstanding (in dollars per share) $ 150.38us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Average remaining life of options outstanding (in years) 9 years 8 months 12 days    
Exercisable options (in shares) 0us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Average exercise price of exercisable options (in dollars per share) $ 0us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange8Member
   
Exercise Price Range 9 [Member]      
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]      
Exercise price range, lower range limit (in dollars per share) $ 31.66us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Exercise price range, upper range limit (in dollars per share) $ 158.30us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Options outstanding (in shares) 2,981,111us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfOutstandingOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Average exercise price of options outstanding (in dollars per share) $ 90.48us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Average remaining life of options outstanding (in years) 6 years 4 months 24 days    
Exercisable options (in shares) 1,811,238us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Average exercise price of exercisable options (in dollars per share) $ 68.02us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeExercisableOptionsWeightedAverageExercisePrice1
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= rop_ExercisePriceRange9Member
   
Earliest [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Percentage of market value at which stock option are granted (in hundredths) 100.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
   
Employee Stock Options [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock based compensation expense 16,600,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
16,900,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
14,800,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Expiration period (in years) 10 years    
Employee Stock Options [Member] | Earliest [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period (in years) 3 years    
Employee Stock Options [Member] | Latest [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period (in years) 5 years    
Restricted Stock [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock based compensation expense $ 46,400,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 36,500,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 25,900,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Restricted Stock [Member] | Earliest [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period (in years) 1 year    
Restricted Stock [Member] | Latest [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period (in years) 3 years    
2006 Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Shares available for grant (in shares) 4,494,756us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= rop_IncentivePlan2006Member
   
2006 Plan [Member] | Employee Stock Options [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of shares reserved for issuance 14,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_PlanNameAxis
= rop_IncentivePlan2006Member
   
Shares available for grant (in shares) 17,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
/ us-gaap_PlanNameAxis
= rop_IncentivePlan2006Member