Revenues from Contracts (Contract Balances) (Details) - USD ($) $ in Millions	3 Months Ended
Mar. 31, 2020	Dec. 31, 2019
Revenue from Contract with Customer [Abstract]
Unbilled receivables	$ 225.3	$ 183.5
Contract liabilities - current	(836.0)	(840.8)
Deferred revenue - non-current	(32.6)	(33.2)
Net contract assets/(liabilities)	(643.3)	$ (690.5)
Change in unbilled receivables	41.8
Change in contract liabilities - current	4.8
Change in deferred revenue - non-current	0.6
Change in net contract assets/(liabilities)	$ 47.2

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

+ References

No definition available.

+ Details

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

- Definition

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

+ References

No definition available.

+ Details

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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

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

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

- References

No definition available.

+ Details

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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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 912
-SubTopic 310
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=118261985&loc=d3e55302-109406

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-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

+ Details

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Balance Type:	debit
Period Type:	instant