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Business Acquisitions (Details) (USD $)
12 Months Ended 4 Months Ended
Dec. 31, 2014
Business
Dec. 31, 2013
Business
Dec. 31, 2012
Business
Dec. 31, 2012
Business Acquisition [Line Items]        
Number of business acquired 3us-gaap_NumberOfBusinessesAcquired 2us-gaap_NumberOfBusinessesAcquired 6us-gaap_NumberOfBusinessesAcquired  
Fair value of assets acquired and liabilities assumed [Abstract]        
Intangible Assets Other than Goodwill   $ 493,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill    
Goodwill 4,710,691,000us-gaap_Goodwill 4,549,998,000us-gaap_Goodwill 3,868,857,000us-gaap_Goodwill 3,868,857,000us-gaap_Goodwill
Intangibles acquired   493,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill    
Finite lived intangible assets   465,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles    
Weighted average useful life   19 years    
Cost of acquired entity transaction costs   3,300,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts    
Trade Names [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Indefinite lived intangible assets   28,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_TradeNamesMember
   
Customer Relationships [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets   451,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
   
Weighted average useful life   20 years    
Technology [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets   12,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_PatentedTechnologyMember
   
Weighted average useful life   7 years    
Noncompete Agreements [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets   2,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_NoncompeteAgreementsMember
   
Weighted average useful life   5 years    
Immaterial Acquisitions [Member]        
Business Acquisition [Line Items]        
Number of business acquired     5us-gaap_NumberOfBusinessesAcquired
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
 
Cost of acquired entity purchase price 303,000,000us-gaap_BusinessCombinationConsiderationTransferred1
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  62,000,000us-gaap_BusinessCombinationConsiderationTransferred1
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
 
Fair value of assets acquired and liabilities assumed [Abstract]        
Intangible Assets Other than Goodwill 99,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  43,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
43,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Goodwill 208,000,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  16,000,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
16,000,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Indefinite lived intangible assets 7,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
     
Intangibles acquired 99,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  43,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
43,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Finite lived intangible assets 92,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  42,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
42,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Weighted average useful life 17 years   7 years  
Cost of acquired entity transaction costs 2,800,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
  1,000,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
1,000,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Immaterial Acquisitions [Member] | Trade Names [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Indefinite lived intangible assets     1,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_TradeNamesMember
1,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_TradeNamesMember
Immaterial Acquisitions [Member] | Backlog [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets 1,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rop_BacklogMember
     
Weighted average useful life 1 year      
Immaterial Acquisitions [Member] | Customer Relationships [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets 82,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
  17,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
17,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
Weighted average useful life 19 years   7 years  
Immaterial Acquisitions [Member] | Technology [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets 7,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_PatentedTechnologyMember
     
Weighted average useful life 6 years      
Immaterial Acquisitions [Member] | Software [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets 2,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_ComputerSoftwareIntangibleAssetMember
     
Weighted average useful life 4 years      
Immaterial Acquisitions [Member] | Unpatented Technology [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets     8,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_UnpatentedTechnologyMember
8,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_UnpatentedTechnologyMember
Weighted average useful life     8 years  
Immaterial Acquisitions [Member] | Patents and other protective rights Memeber        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets     16,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_PatentsMember
16,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_PatentsMember
Weighted average useful life     7 years  
Advanced Sensors, Ltd [Member]        
Business Acquisition [Line Items]        
Cost of acquired entity purchase price   54,000,000us-gaap_BusinessCombinationConsiderationTransferred1
/ us-gaap_BusinessAcquisitionAxis
= rop_AdvancedSensorsLtdMember
   
Fair value of assets acquired and liabilities assumed [Abstract]        
Goodwill   28,000,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_AdvancedSensorsLtdMember
   
Indefinite lived intangible assets   28,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_AdvancedSensorsLtdMember
   
Managed Health Care Associates, Inc [Member]        
Business Acquisition [Line Items]        
Cost of acquired entity purchase price   1,000,000,000us-gaap_BusinessCombinationConsiderationTransferred1
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Fair value of assets acquired and liabilities assumed [Abstract]        
Current assets   59,813,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Intangible Assets Other than Goodwill   465,500,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Goodwill   678,183,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Other assets   5,798,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Total assets acquired   1,209,294,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Current liabilities   (24,717,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Long-term deferred tax liability   (162,503,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Other liabilities   (6,524,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Net assets acquired   1,015,550,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Fair value adjustment for admin fees related to customer purchases   35,000,000us-gaap_AssetsFairValueAdjustment
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Fair value liability related revenue-share obligation   8,600,000us-gaap_LiabilitiesFairValueAdjustment
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Intangibles acquired   465,500,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_ManagedHealthCareAssociatesIncMember
   
Sunquest Information Systems, Inc [Member]        
Business Acquisition [Line Items]        
Cost of acquired entity purchase price     1,400,000,000us-gaap_BusinessCombinationConsiderationTransferred1
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
 
Fair value of assets acquired and liabilities assumed [Abstract]        
Current assets     96,883,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
96,883,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Intangible Assets Other than Goodwill     669,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
669,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Goodwill     993,780,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
993,780,000us-gaap_Goodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Other assets     2,694,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
2,694,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Total assets acquired     1,762,357,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
1,762,357,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Deferred revenue     (83,065,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesDeferredRevenue
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
(83,065,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesDeferredRevenue
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Other current liabilities     (18,762,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
(18,762,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Long-term deferred tax liability     (244,550,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
(244,550,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Net assets acquired     1,415,980,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
1,415,980,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Intangibles acquired     669,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
669,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Finite lived intangible assets     571,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
571,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Weighted average useful life     18 years  
Cost of acquired entity transaction costs     6,700,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
6,700,000us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Pro Forma Sales     3,130,407us-gaap_BusinessAcquisitionsProFormaRevenue
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
69,400,000us-gaap_BusinessAcquisitionsProFormaRevenue
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Pro forma Net income     521,141us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
8,800,000us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
Pro Forma Earnings per share, basic (in dollars per share)     $ 5.33us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
 
Pro Forma Earnings per share, diluted (in dollars per share)     $ 5.23us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
 
Pro Forma Earnings Adjustment for non-recurring acquisition and other costs     50,700,000rop_BusinessAcquisitionProFormaEarningsAdjustmentForNonRecurringAcquisitionAndOtherCosts
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
 
Sunquest Information Systems, Inc [Member] | Trade Names [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Indefinite lived intangible assets     98,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_TradeNamesMember
98,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_TradeNamesMember
Sunquest Information Systems, Inc [Member] | Customer Relationships [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets     460,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
460,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
Weighted average useful life     20 years  
Sunquest Information Systems, Inc [Member] | Software [Member]        
Fair value of assets acquired and liabilities assumed [Abstract]        
Finite lived intangible assets     $ 111,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_ComputerSoftwareIntangibleAssetMember
$ 111,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
/ us-gaap_BusinessAcquisitionAxis
= rop_SunquestInformationSystemsIncMember
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_ComputerSoftwareIntangibleAssetMember
Weighted average useful life     12 years