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Income Taxes (Details) (USD $)
 12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Income (Loss) from Continuing Operations before Equity Method Investments, Income Taxes, Extraordinary Items, Noncontrolling Interest [Abstract]      
United States $ 665,219,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic $ 517,432,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic $ 430,573,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic
Other 256,237,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign 236,698,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign 256,108,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign
Earnings Before Income Taxes 921,456,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 754,130,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments 686,681,000us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments
Current:      
Federal 218,302,000us-gaap_CurrentFederalTaxExpenseBenefit 166,430,000us-gaap_CurrentFederalTaxExpenseBenefit 136,860,000us-gaap_CurrentFederalTaxExpenseBenefit
State 37,155,000us-gaap_CurrentStateAndLocalTaxExpenseBenefit 12,577,000us-gaap_CurrentStateAndLocalTaxExpenseBenefit 9,972,000us-gaap_CurrentStateAndLocalTaxExpenseBenefit
Foreign 56,107,000us-gaap_CurrentForeignTaxExpenseBenefit 40,451,000us-gaap_CurrentForeignTaxExpenseBenefit 48,403,000us-gaap_CurrentForeignTaxExpenseBenefit
Deferred:      
Federal (30,664,000)us-gaap_DeferredFederalIncomeTaxExpenseBenefit (1,965,000)us-gaap_DeferredFederalIncomeTaxExpenseBenefit 15,789,000us-gaap_DeferredFederalIncomeTaxExpenseBenefit
Foreign (5,477,000)us-gaap_DeferredForeignIncomeTaxExpenseBenefit (1,656,000)us-gaap_DeferredForeignIncomeTaxExpenseBenefit (7,703,000)us-gaap_DeferredForeignIncomeTaxExpenseBenefit
Total Income Taxes 275,423,000us-gaap_IncomeTaxExpenseBenefit 215,837,000us-gaap_IncomeTaxExpenseBenefit 203,321,000us-gaap_IncomeTaxExpenseBenefit
Federal Statutory Tax Rate Reconciliation      
Federal statutory rate (in hundredths) 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
Foreign rate differential (in hundredths) (3.90%)us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential (4.10%)us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential (3.90%)us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential
R&D tax credits (in hundredths) (0.40%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch (0.50%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch 0.00%us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch
State taxes, net of federal benefit (in hundredths) 2.00%us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes 1.90%us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes 1.70%us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes
Foreign tax credits (in hundredths) 0.00%us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsForeign 0.00%us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsForeign (2.40%)us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsForeign
Section 199 deduction (in hundredths) (1.60%)us-gaap_EffectiveIncomeTaxRateReconciliationDeductionsQualifiedProductionActivities (1.80%)us-gaap_EffectiveIncomeTaxRateReconciliationDeductionsQualifiedProductionActivities (1.30%)us-gaap_EffectiveIncomeTaxRateReconciliationDeductionsQualifiedProductionActivities
Other, net (in hundredths) (1.20%)us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments (1.90%)us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments 0.50%us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments
Effective Rate (in hundredths) 29.90%us-gaap_EffectiveIncomeTaxRateContinuingOperations 28.60%us-gaap_EffectiveIncomeTaxRateContinuingOperations 29.60%us-gaap_EffectiveIncomeTaxRateContinuingOperations
Deferred tax assets:      
Reserves and accrued expenses 130,508,000us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccruals 119,955,000us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccruals  
Inventories 10,186,000us-gaap_DeferredTaxAssetsInventory 10,315,000us-gaap_DeferredTaxAssetsInventory  
Net operating loss carryforwards 41,480,000us-gaap_DeferredTaxAssetsOperatingLossCarryforwards 35,286,000us-gaap_DeferredTaxAssetsOperatingLossCarryforwards  
R&D credits 7,145,000us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch 3,134,000us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch  
Foreign tax credits 0us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign 425,000us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign  
Valuation allowance (16,169,000)us-gaap_DeferredTaxAssetsValuationAllowance (5,917,000)us-gaap_DeferredTaxAssetsValuationAllowance  
Total deferred tax assets 173,150,000us-gaap_DeferredTaxAssetsNet 163,198,000us-gaap_DeferredTaxAssetsNet  
Deferred tax liabilities:      
Reserves and accrued expenses 27,981,000rop_DeferredTaxLiabilitiesTaxDeferredExpenseReservesAndAccruals 20,995,000rop_DeferredTaxLiabilitiesTaxDeferredExpenseReservesAndAccruals  
Amortizable intangible assets 798,502,000us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets 826,838,000us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets  
Plant and equipment 4,741,000us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment 12,423,000us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment  
Total deferred tax liabilities 831,224,000us-gaap_DeferredTaxLiabilities 860,256,000us-gaap_DeferredTaxLiabilities  
Reconciliation of Unrecognized Tax Benefits [Roll Forward]      
Beginning balance 26,924,000us-gaap_UnrecognizedTaxBenefits 24,865,000us-gaap_UnrecognizedTaxBenefits 19,556,000us-gaap_UnrecognizedTaxBenefits
Additions for tax positions of prior periods 6,532,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions 3,055,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions 1,371,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions
Additions for tax positions of the current period 5,571,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions 1,639,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions 1,541,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions
Additions due to acquisitions 0us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromAcquisition 5,026,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromAcquisition 9,116,000us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromAcquisition
Reductions for tax positions of prior periods (1,008,000)us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions (3,675,000)us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions (197,000)us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions
Settlements with taxing authorities (518,000)us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromSettlementsWithTaxingAuthorities 0us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromSettlementsWithTaxingAuthorities 0us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromSettlementsWithTaxingAuthorities
Lapse of applicable statute of limitations (8,934,000)us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations (3,986,000)us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations (6,522,000)us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations
Ending balance 28,567,000us-gaap_UnrecognizedTaxBenefits 26,924,000us-gaap_UnrecognizedTaxBenefits 24,865,000us-gaap_UnrecognizedTaxBenefits
Unrecognized income tax benefits that, if recognized, would affect the effective income tax rate in any future periods 27,000,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate    
Interest and penalties related to unrecognized tax benefits 600,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense    
Accrued interest and penalties 5,200,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued 4,500,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued  
Reduction in unrecognized tax benefits expected within twelve months of the balance sheet date 9,200,000us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleAmountOfUnrecordedBenefit    
Earliest [Member]      
Operating Loss Carryforwards [Line Items]      
Tax Credit Carryforward, Expiration Date Dec. 31, 2019    
Latest [Member]      
Operating Loss Carryforwards [Line Items]      
Tax Credit Carryforward, Expiration Date Dec. 31, 2034    
Internal Revenue Service (IRS) [Member]      
Operating Loss Carryforwards [Line Items]      
Net operating loss carryforwards 14,100,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_InternalRevenueServiceIRSMember		    
Operating Loss Carryforwards, Valuation Allowance 11,900,000us-gaap_OperatingLossCarryforwardsValuationAllowance
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_InternalRevenueServiceIRSMember		    
Internal Revenue Service (IRS) [Member] | Earliest [Member]      
Operating Loss Carryforwards [Line Items]      
Operating loss carryover expiration date Dec. 31, 2023    
Internal Revenue Service (IRS) [Member] | Latest [Member]      
Operating Loss Carryforwards [Line Items]      
Operating loss carryover expiration date Dec. 31, 2034    
Foreign Tax Authority [Member]      
Operating Loss Carryforwards [Line Items]      
Net operating loss carryforwards 6,600,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember		    
Operating Loss Carryforwards, Valuation Allowance 4,300,000us-gaap_OperatingLossCarryforwardsValuationAllowance
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember		    
Foreign Tax Authority [Member] | Earliest [Member]      
Operating Loss Carryforwards [Line Items]      
Operating loss carryover expiration date Dec. 31, 2015    
State and Local Jurisdiction [Member]      
Operating Loss Carryforwards [Line Items]      
Net operating loss carryforwards 20,800,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_StateAndLocalJurisdictionMember		    
State and Local Jurisdiction [Member] | Earliest [Member]      
Operating Loss Carryforwards [Line Items]      
Operating loss carryover expiration date Dec. 31, 2021    
State and Local Jurisdiction [Member] | Latest [Member]      
Operating Loss Carryforwards [Line Items]      
Operating loss carryover expiration date Dec. 31, 2034    
Research Tax Credit Carryforward [Member]      
Operating Loss Carryforwards [Line Items]      
Tax Credit Carryforward, Amount $ 7,100,000us-gaap_TaxCreditCarryforwardAmount
/ us-gaap_TaxCreditCarryforwardAxis
= us-gaap_ResearchMember