Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (a)(3)
-URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16265-109275

+ Details

Name:	us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_BusinessAcquisitionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of consideration transferred, consisting of acquisition-date fair value of assets transferred by the acquirer, liabilities incurred by the acquirer, and equity interest issued by the acquirer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=126966197&loc=d3e6613-128477

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126975305&loc=d3e6927-128479

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 7
-URI https://asc.fasb.org/extlink&oid=126966197&loc=d3e6578-128477

+ Details

Name:	us-gaap_BusinessCombinationConsiderationTransferred1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of assets, excluding financial assets and goodwill, that lack physical substance, having a projected indefinite period of benefit, acquired at the acquisition date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=128092470&loc=d3e4845-128472

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of intangible assets, excluding goodwill, acquired at the acquisition date.

+ References

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of gain (loss) on sale or disposal of an equity method investment.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(b)(7)(c))
-URI https://asc.fasb.org/extlink&oid=126953954&loc=SL114868664-224227

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(b)(9)(a))
-URI https://asc.fasb.org/extlink&oid=126953954&loc=SL114868664-224227

+ Details

Name:	us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(1))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (h)
-URI https://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 55
-Paragraph 24
-URI https://asc.fasb.org/extlink&oid=122137925&loc=d3e14258-109268

Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI https://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(15))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_Goodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

The number of businesses acquired by the entity during the period.

+ References

No definition available.

+ Details

Name:	us-gaap_NumberOfBusinessesAcquired
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

The cash inflow associated with the sale of equity method investments, which are investments in joint ventures and entities in which the entity has an equity ownership interest normally of 20 to 50 percent and exercises significant influence.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 12
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3179-108585

+ Details

Name:	us-gaap_ProceedsFromSaleOfEquityMethodInvestments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=rop_ApplicationSoftwareSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis=rop_SedaruIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_HorizonLabSystemsLLCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_CommonCentsSystemsIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_MGASystemsHoldingsIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_ViDesktopIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_TIPTechnologiesIncAndCommonSenseSolutionsIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_HorizonLabSystemsLLCCommonCentsSystemsIncAndMGASystemsHoldingsIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_TradeNamesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_CustomerRelationshipsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_TechnologyBasedIntangibleAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=rop_FrontlineTechnologiesParentLLCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Business Acquisitions and Disposition (Details) $ in Thousands							3 Months Ended	9 Months Ended
	Oct. 04, 2022 USD ($)	Aug. 19, 2022 USD ($)	Jun. 27, 2022 USD ($)	Apr. 06, 2022 USD ($)	Jan. 03, 2022 USD ($)	Mar. 17, 2021 USD ($)	Sep. 30, 2022 USD ($) business	Sep. 30, 2022 USD ($)	Dec. 31, 2021 USD ($)
Business Acquisition [Line Items]
Goodwill							$ 13,672,800	$ 13,672,800	$ 13,476,300
Application Software
Business Acquisition [Line Items]
Goodwill							9,191,000	9,191,000	$ 8,889,300
Sedaru, Inc.
Business Acquisition [Line Items]
Proceeds from sale of equity method investments						$ 27,100
Equity method investment, realized gain (loss) on disposal						$ 27,100
Horizon Lab Systems, LLC
Business Acquisition [Line Items]
Aggregate purchase price					$ 49,800
Common Cents Systems, Inc
Business Acquisition [Line Items]
Aggregate purchase price				$ 25,500
MGA Systems Holdings, Inc
Business Acquisition [Line Items]
Aggregate purchase price			$ 180,100
viDesktop Inc \| Application Software
Business Acquisition [Line Items]
Aggregate purchase price		$ 286,500
TIP Technologies Inc and Common Sense Solutions Inc \| Application Software
Business Acquisition [Line Items]
Aggregate purchase price							$ 36,900
Number of business acquisitions \| business							2
Horizon Lab Systems, LLC , Common Cents Systems, Inc and MGA Systems Holdings, Inc
Business Acquisition [Line Items]
Goodwill							$ 361,500	361,500
Other identifiable intangibles							239,300	239,300
Horizon Lab Systems, LLC , Common Cents Systems, Inc and MGA Systems Holdings, Inc \| Trade names
Business Acquisition [Line Items]
Intangible assets acquired, not subject to amortization							9,500	9,500
Horizon Lab Systems, LLC , Common Cents Systems, Inc and MGA Systems Holdings, Inc \| Customer related intangibles
Business Acquisition [Line Items]
Other identifiable intangibles							223,400	$ 223,400
Weighted average useful life of finite-lived intangible assets (in years)								18 years 2 months 12 days
Horizon Lab Systems, LLC , Common Cents Systems, Inc and MGA Systems Holdings, Inc \| Technology
Business Acquisition [Line Items]
Other identifiable intangibles							$ 15,900	$ 15,900
Weighted average useful life of finite-lived intangible assets (in years)								4 years 10 months 24 days
Frontline Technologies Parent, LLC \| Subsequent Event
Business Acquisition [Line Items]
Aggregate purchase price	$ 3,738