Revenues from Contracts - Contract Balances (Details) - USD ($) $ in Millions	9 Months Ended
Sep. 30, 2022	Dec. 31, 2021
Revenue from Contract with Customer [Abstract]
Unbilled receivables	$ 98.8	$ 81.9
Change in unbilled receivables	16.9
Deferred revenue - current	(1,048.8)	(1,106.3)
Change in deferred revenue - current	57.5
Deferred revenue - non-current	(89.0)	(69.9)
Change in deferred revenue - non-current	(19.1)
Net contract assets/(liabilities)	(1,039.0)	$ (1,094.3)
Change in net contract assets/(liabilities)	$ 55.3

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, Current, Increase (Decrease)

+ References

No definition available.

+ Details

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

- 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 current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130531-203044

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130532-203044

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 https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

+ Details

Name:	us-gaap_ContractWithCustomerLiabilityCurrent
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/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126919976&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 https://asc.fasb.org/extlink&oid=126919976&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 https://asc.fasb.org/extlink&oid=126920106&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

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
-Publisher FASB
-Name Accounting Standards Codification
-Topic 912
-SubTopic 310
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126938201&loc=d3e55302-109406

+ Details

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