Leases (Lease Balances Within Balance Sheet) (Details) $ in Millions	Sep. 30, 2019 USD ($)
ASSETS:
Operating lease ROU assets	$ 276.9
LIABILITIES:
Current operating lease liabilities	56.4
Operating lease liabilities	229.7
Total operating lease liabilities	$ 286.1

Assets, Lessee [Abstract]

No definition available.

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- Definition

Liabilities, Lessee [Abstract]

+ References

No definition available.

+ Details

Name:	rop_LiabilitiesLesseeAbstract
Namespace Prefix:	rop_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=77888419&loc=SL77918627-209977

+ Details

Name:	us-gaap_OperatingLeaseLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease, classified as current.

+ References

+ Details

Name:	us-gaap_OperatingLeaseLiabilityCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease, classified as noncurrent.

+ References

+ Details

Name:	us-gaap_OperatingLeaseLiabilityNoncurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's right to use underlying asset under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=77888419&loc=SL77918627-209977

+ Details

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