Contract Balances (Contract Balances) (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2018	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016	Jan. 01, 2018
Revenue from Contract with Customer [Abstract]
Unbilled receivables - current	$ 169.4	$ 169.4			$ 149.1
Contract liabilities - current	(714.1)	(714.1)			(605.5)
Deferred revenue - non-current	(29.8)	(29.8)			(31.8)
Net contract assets/(liabilities)	(574.5)	(574.5)			$ (488.2)
Change in unbilled receivables - current	20.3	$ 14.0	$ 13.5	$ 1.2
Change in contract liabilities - current	(108.6)
Change in deferred revenue - non-current	2.0
Change in net contract assets/(liabilities)	$ (86.3)

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

No definition available.

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

- Definition

Deferred Revenue, Billings In-Excess Of Revenues, And Customer Deposits

+ References

No definition available.

+ Details

Name:	rop_DeferredRevenueBillingsInExcessOfRevenuesAndCustomerDeposits
Namespace Prefix:	rop_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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, Liability

+ References

No definition available.

+ Details

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

- Definition

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

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=82913815&loc=SL49130532-203044

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=82913847&loc=SL49130549-203045

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=82913815&loc=SL49130531-203044

+ Details

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

- 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/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=82913815&loc=SL49130531-203044

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=82913847&loc=SL49130549-203045

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=82913815&loc=SL49130532-203044

+ Details

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

- Definition

The increase (decrease) during the reporting period of the amount of revenue for work performed for which billing has not occurred, net of uncollectible accounts.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=98514028&loc=d3e3602-108585

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Unbilled amounts due for services rendered or to be rendered, actions taken or to be taken, or a promise to refrain from taking certain actions in accordance with the terms of a legally binding agreement between the entity and, at a minimum, one other party. An example would be amounts associated with contracts or programs where the recognized revenue for performance thereunder exceeds the amounts billed under the terms thereof as of the date of the balance sheet.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.3(c)(3))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 912
-SubTopic 310
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=68054760&loc=d3e55302-109406

+ Details

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