Leases (Lease Maturities) (Details) - USD ($) $ in Millions	Jan. 01, 2022	Jan. 02, 2021
Operating Leases
2022	$ 34.8
2023	26.7
2024	20.7
2025	16.2
2026	13.4
Thereafter	36.0
Total Lease Payments	147.8
Less: Interest	$ (31.1)
Finance Lease, Liability, Statement of Financial Position [Extensible Enumeration]	Net Property, Plant and Equipment	Net Property, Plant and Equipment
Present Value of Lease Liabilities	$ 116.7
Finance Leases
2022	6.8
2023	6.9
2024	7.0
2025	7.0
2026	7.0
Thereafter	83.0
Total Lease Payments	117.7
Less: Interest	(41.5)
Present Value of Lease Liabilities	76.2
Total
2022	41.6
2023	33.6
2024	27.7
2025	23.2
2026	20.4
Thereafter	119.0
Total Lease Payments	265.5
Less: Interest	(72.6)
Present Value of Lease Liabilities	$ 192.9

Lease Liabilities, Payments Due [Abstract]

No definition available.

Name:	rbc_LeaseLiabilitiesPaymentsDueAbstract
Namespace Prefix:	rbc_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Lease, Liability

+ References

No definition available.

+ Details

Name:	rbc_LeaseLiability
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDue
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due Year Five

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueYearFive
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due Year Four

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueYearFour
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due Year One

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueYearOne
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due Year Three

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueYearThree
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due Year Two

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueYearTwo
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Payments, Due after Year Five

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityPaymentsDueafterYearFive
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lessee, Liability, Undiscounted Excess Amount

+ References

No definition available.

+ Details

Name:	rbc_LesseeLiabilityUndiscountedExcessAmount
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from finance lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918701-209980

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments for finance lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid after fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Indicates line item in statement of financial position that includes finance lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123391704&loc=SL77918631-209977

+ Details

Name:	us-gaap_FinanceLeaseLiabilityStatementOfFinancialPositionExtensibleList
Namespace Prefix:	us-gaap_
Data Type:	enum2:enumerationSetItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for finance lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease due after fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating lease.

+ References

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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