Revenues from Contracts (Contract Balances) (Details) - USD ($) $ in Millions	9 Months Ended
Sep. 30, 2019	Dec. 31, 2018
Revenue from Contract with Customer [Abstract]
Unbilled receivables	$ 197.8	$ 169.4
Contract liabilities - current	(771.6)	(714.1)
Deferred revenue - non-current	(28.9)	(29.8)
Net contract assets/(liabilities)	(602.7)	$ (574.5)
Change in unbilled receivables	28.4
Change in contract liabilities - current	(57.5)
Change in deferred revenue - non-current	0.9
Change in net contract assets/(liabilities)	$ (28.2)

Contract With Customer, Asset, Net, Increase (Decrease)

No definition available.

Name:	rop_ContractWithCustomerAssetNetIncreaseDecrease
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Contract With Customer, Liability, Deferred Revenue, Billings In-Excess Of Revenues, And Customer Deposits, Current

+ References

No definition available.

+ Details

Name:	rop_ContractWithCustomerLiabilityDeferredRevenueBillingsInExcessOfRevenuesAndCustomerDepositsCurrent
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Contract With Customer, Liability, Noncurrent, Increase (Decrease)

+ References

No definition available.

+ Details

Name:	rop_ContractWithCustomerLiabilityNoncurrentIncreaseDecrease
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Contract With Customer, Net Asset (Liability)

+ References

No definition available.

+ Details

Name:	rop_ContractWithCustomerNetAssetLiability
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Deferred Revenue, Billings In-Excess Of Revenues, And Customer Deposits, Increase (Decrease)

+ References

No definition available.

+ Details

Name:	rop_DeferredRevenueBillingsInExcessOfRevenuesAndCustomerDepositsIncreaseDecrease
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Increase (Decrease) In Contract With Customer, Asset (Liability)

+ References

No definition available.

+ Details

Name:	rop_IncreaseDecreaseInContractWithCustomerAssetLiability
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable, classified as noncurrent.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=118944033&loc=SL49130532-203044

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=118944033&loc=SL49130531-203044

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=118956577&loc=SL49130549-203045

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount received for services rendered and products shipped, but not yet billed, for non-contractual agreements due within one year or the normal operating cycle, if longer.

+ References

No definition available.

+ Details

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