Retirement and Post Retirement Plans (Level 3 Plan Assets) (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 02, 2016	Jan. 03, 2015
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair value of plan assets at beginning of period	$ 126.6
Fair value of plan assets at end of period	162.1	$ 126.6
Level 3
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair value of plan assets at beginning of period	11.5	10.1
Acquisition	1.0	0.0
Net purchases	1.9	0.7
Net gains	0.1	0.7
Fair value of plan assets at end of period	14.5	11.5
Real Estate [Member]
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair Value	$ 8.1	$ 6.2
Minimum [Member] \| Level 3
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair Value Inputs, Exit Capitalization Rate	4.90%	5.30%
Fair Value Inputs, Discount Rate	6.60%	6.80%
Maximum [Member] \| Level 3
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Fair Value Inputs, Exit Capitalization Rate	7.00%	7.50%
Fair Value Inputs, Discount Rate	8.30%	9.50%

Fair Value Inputs, Exit Capitalization Rate

No definition available.

Name:	rbc_FairValueInputsExitCapitalizationRate
Namespace Prefix:	rbc_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Assets, usually stocks, bonds, and other investments, that have been segregated and restricted (usually in a trust) to provide benefits, at their fair value as of the measurement date. Plan assets include amounts contributed by the employer (and by employees for a contributory plan) and amounts earned from investing the contributions, less benefits paid. If a plan has liabilities other than for benefits, those non-benefit obligations may be considered as reductions of plan assets.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 30
-Section 35
-Paragraph 50
-URI http://asc.fasb.org/extlink&oid=49178875&loc=d3e12355-114930

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=58740216&loc=d3e1928-114920

+ Details

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

- Definition

Interest rate used to find the present value of an amount to be paid or received in the future as an input to measure fair value. For example, but not limited to, weighted average cost of capital (WACC), cost of capital, cost of equity and cost of debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)
-URI http://asc.fasb.org/extlink&oid=36462937&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueInputsDiscountRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of purchases of financial instrument classified as an asset measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-URI http://asc.fasb.org/extlink&oid=36462937&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of sale of financial instrument classified as an asset measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-URI http://asc.fasb.org/extlink&oid=36462937&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Fair value of financial instrument classified as an asset measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=36462937&loc=d3e19207-110258

+ Details

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

- Definition

Amount of gain (loss) recognized in other comprehensive income (loss) for financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1a)
-URI http://asc.fasb.org/extlink&oid=36462937&loc=d3e19207-110258

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_RealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RangeAxis=us-gaap_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RangeAxis=us-gaap_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: