Contingencies (Details) $ in Millions	12 Months Ended
Jan. 02, 2021 USD ($) subsidiary	Dec. 28, 2019 USD ($)
Commitments and Contingencies Disclosure [Abstract]
Number of subsidiaries involved in litigation \| subsidiary	1
Movement in Standard Product Warranty Accrual [Roll Forward]
Beginning Balance	$ 15.1	$ 14.8
Less: Payments	16.7	14.5
Provisions	16.9	15.2
Held for Sale	0.0	(0.4)
Translation Adjustments	0.2	0.0
Ending Balance	$ 15.5	$ 15.1

Number of Subsidiaries Involved in Litigation

No definition available.

Name:	rbc_NumberOfSubsidiariesInvolvedInLitigation
Namespace Prefix:	rbc_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Standard Product Warranty Accrual, Held-For-Sale

+ References

No definition available.

+ Details

Name:	rbc_StandardProductWarrantyAccrualHeldForSale
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

Amount as of the balance sheet date of the aggregate standard product warranty liability. Does not include the balance for the extended product warranty liability.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (c)(1),(c)(5)
-URI http://asc.fasb.org/extlink&oid=68068213&loc=d3e12565-110249

+ Details

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

- Definition

Amount of foreign currency translation gain (loss) which decreases (increases) the standard product warranty accrual. Excludes extended product warranties.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=68068213&loc=d3e12565-110249

+ Details

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

- Definition

Amount of decrease in the standard product warranty accrual from payments made in cash or in kind to satisfy claims under the terms of the standard product warranty. Excludes extended product warranties.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph ((c)(2))
-URI http://asc.fasb.org/extlink&oid=68068213&loc=d3e12565-110249

+ Details

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

- Definition

Amount of increase in the standard product warranty accrual from warranties issued. Excludes extended product warranties.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph ((c)(3))
-URI http://asc.fasb.org/extlink&oid=68068213&loc=d3e12565-110249

+ Details

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