Receivables - Rollforward of Combined Allowances for Doubtful Accounts Related to Trade and Other Accounts Receivable (Detail) - USD ($) $ in Millions	12 Months Ended
Jan. 01, 2022	Jan. 02, 2021
Allowances for credit losses:
Beginning of period	$ 26.3	$ 20.9
Provision for credit losses	15.5	18.9
Charge-offs	(13.6)	(13.6)
Recoveries	0.0	0.2
Currency translation	(0.9)	(0.1)
End of period	$ 27.3	$ 26.3

Accounts Receivable, Allowance For Credit Loss, Foreign Currency Translation Increase (Decrease)

No definition available.

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Namespace Prefix:	sna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of allowance for credit loss on accounts receivable, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(4)
-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 310
-SubTopic 10
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=123577603&loc=d3e5074-111524

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=124255206&loc=SL82895884-210446

+ Details

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

- Definition

Amount of increase in allowance for credit loss on accounts receivable, from recovery.

+ References

+ Details

Name:	us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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

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

- Definition

Amount of direct write-downs of accounts receivable charged against the allowance.

+ References

+ Details

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

- Definition

Amount of expense (reversal of expense) for expected credit loss on accounts receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(5))
-URI http://asc.fasb.org/extlink&oid=123367319&loc=SL114868664-224227

+ Details

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