Fair Value of Financial Instruments (Details) $ in Millions	3 Months Ended
Mar. 31, 2016 USD ($)
Convertible Notes [Member]
Short-term Debt [Line Items]
Fair Value of Debt Instrument	$ 4
Fair Value, Inputs, Level 2 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	3,100
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2017 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	400
Long-term Debt, Fair Value	$ 401
Notes due	2017
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2018 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	$ 800
Long-term Debt, Fair Value	$ 816
Notes due	2018
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2019 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	$ 500
Long-term Debt, Fair Value	$ 558
Notes due	2019
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2020 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	$ 600
Long-term Debt, Fair Value	$ 614
Notes due	2020
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2022 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	$ 500
Long-term Debt, Fair Value	$ 503
Notes due	2022
Fair Value, Inputs, Level 2 [Member] \| Senior notes due 2025 [Member]
Debt Instrument [Line Items]
Face Value of Debt Instrument	$ 300
Long-term Debt, Fair Value	$ 312
Notes due	2025

Year when the debt instrument is scheduled to be fully repaid.

No definition available.

Name:	rop_DebtInstrumentMaturityYear
Namespace Prefix:	rop_
Data Type:	xbrli:gYearItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=34725769&loc=d3e28878-108400

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=6451184&loc=d3e28551-108399

+ Details

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

- Definition

Fair value portion of debt instrument payable, including, but not limited to, notes payable and loans payable.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=49121117&loc=d3e13433-108611

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=49121117&loc=d3e13476-108611

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

The fair value amount of long-term debt whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission.

+ References

No definition available.

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Details

Name:	us-gaap_ShortTermDebtTypeAxis=rop_ConvertibleSubordinatedNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2017Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2018Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2019Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2020Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2022Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=rop_SeniorNotesDue2025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: