Income Taxes (Deferred Tax Asset (Liability)) (Details) - USD ($) $ in Millions	Jan. 01, 2022	Jan. 02, 2021
Income Tax Disclosure [Abstract]
Accrued Benefits	$ 55.7	$ 36.8
Bad Debt Allowances	6.9	4.9
Warranty Accruals	4.6	3.4
Inventory	(2.0)
Inventory		10.4
Tax Loss Carryforward	8.8	9.2
Operating Lease Liability	49.8	18.8
Other	44.4	34.6
Deferred Tax Assets before Valuation Allowance	168.2	118.1
Valuation Allowance	(5.3)	(7.4)
Total Deferred Tax Assets	162.9	110.7
Property Related	(77.0)	(33.7)
Intangible Items	(636.2)	(170.9)
Accrued Liabilities	(15.8)	(8.8)
Derivative Instruments	(7.4)	(7.5)
Operating Lease Asset	(42.8)	(17.9)
Deferred Tax Liabilities	(779.2)	(238.8)
Net Deferred Tax Liability	$ 616.3	$ 128.1

Deferred Tax Assets, Operating Lease Liability

No definition available.

Name:	rbc_DeferredTaxAssetsOperatingLeaseLiability
Namespace Prefix:	rbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Deferred Tax Liabilities, Operating Lease Right Of Use Asset

+ References

No definition available.

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(26)(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(15)(b)(2))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15)(2))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(26)(a))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

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

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from inventory.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319

+ Details

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

- Definition

Amount, after allocation of valuation allowances and deferred tax liability, of deferred tax asset attributable to deductible differences and carryforwards, without jurisdictional netting.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

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

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible operating loss carryforwards.

+ References

+ Details

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

- Definition

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences, classified as other.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319

+ Details

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

- Definition

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences from employee benefits, classified as other.

+ References

+ Details

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

- Definition

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary difference from allowance for credit loss on accounts receivable.

+ References

+ Details

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

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from warranty reserves.

+ References

+ Details

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

- Definition

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

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

- Definition

Amount, after deferred tax asset, of deferred tax liability attributable to taxable differences without jurisdictional netting.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 45
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=123427490&loc=d3e31931-109318

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

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

- Definition

Amount of deferred tax consequences attributable to taxable temporary differences derived from inventory.

+ References

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from reserves and accruals.

+ References

No definition available.

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from derivatives.

+ References

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from intangible assets other than goodwill.

+ References

+ Details

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

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from property, plant, and equipment.

+ References

+ Details

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

- References

No definition available.

+ Details

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