Goodwill and Other Intangible Assets (Goodwill) (Details) $ in Millions	6 Months Ended
Jun. 30, 2020 USD ($)
Goodwill [Roll Forward]
Balances	$ 10,815.4
Additions	80.5
Other	(0.1)
Currency translation adjustments	(49.2)
Balances	10,846.6
Application Software
Goodwill [Roll Forward]
Balances	5,389.4
Additions	0.0
Other	0.5
Currency translation adjustments	(12.8)
Balances	5,377.1
Network Software & Systems
Goodwill [Roll Forward]
Balances	3,933.5
Additions	80.5
Other	(0.6)
Currency translation adjustments	(26.8)
Balances	3,986.6
Measurement & Analytical Solutions
Goodwill [Roll Forward]
Balances	1,178.0
Additions	0.0
Other	0.0
Currency translation adjustments	(6.3)
Balances	1,171.7
Process Technologies
Goodwill [Roll Forward]
Balances	314.5
Additions	0.0
Other	0.0
Currency translation adjustments	(3.3)
Balances	$ 311.2

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.

Reference 1: 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 http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=120320667&loc=SL49117168-202975

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

+ Details

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

- Definition

Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

+ Details

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

- Definition

Amount of increase (decrease), classified as other, of an asset representing the future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (g)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

+ Details

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

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Amount of increase (decrease) from foreign currency translation adjustments and purchase accounting adjustments 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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 25
-Paragraph 16
-URI http://asc.fasb.org/extlink&oid=116868678&loc=d3e961-128460

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (g)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

+ Details

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

- Details

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

- Details

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