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Retirement and Other Benefit Plans (Details) $ in Millions | 12 Months Ended
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Dec. 31, 2022 USD ($) plan | Dec. 31, 2021 USD ($) plan | Dec. 31, 2020 USD ($) plan
Retirement Benefits [Abstract] |  |  |
Number of defined contribution plans maintained by the company | plan | 3 | 3 | 3
Defined contribution retirement plan cost | $ | $ 34.1 | $ 30.2 | $ 24.3

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- Definition Number of defined contribution plans maintained by the company. + References No definition available. + Details
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Namespace Prefix: | rop_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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- References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of cost for defined contribution plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 70 -Section 50 -Paragraph 1 -URI https://asc.fasb.org/extlink&oid=49170846&loc=d3e28014-114942 + Details
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Namespace Prefix: | us-gaap_
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