Revenues from Contracts - Schedule of Contract Balances (Details) - USD ($) $ in Millions	9 Months Ended
Sep. 30, 2025	Dec. 31, 2024
Revenue from Contract with Customer [Abstract]
Unbilled receivables	$ 140.9	$ 127.3
Deferred revenue – current	(1,809.1)	(1,737.4)
Deferred revenue - non-current	(168.9)	(154.7)
Net contract assets/(liabilities)	(1,837.1)	$ (1,764.8)
Change in unbilled receivables	13.6
Change in deferred revenue - current	(71.7)
Change in deferred revenue - non-current	(14.2)
Change in net contract assets/(liabilities)	$ (72.3)

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

Name:	rop_ContractWithCustomerLiabilityBillingsInExcessOfRevenuesAndCustomerDepositsIncreaseDecrease
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

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

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
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-11

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-8

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-2

+ 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

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/disclosureRef
-Topic 912
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478345/912-310-45-2

+ Details

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