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Exit and Disposal Activities - Restructuring Accrual Rollforward (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	$ 7.0	$ 10.0
Provision	0.0	0.0
Usage	(4.2)	(3.0)
Restructuring reserve, ending balance	2.8	7.0
Commercial & Industrial Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	4.3	5.8
Provision	0.0	0.0
Usage	(2.7)	(1.5)
Restructuring reserve, ending balance	1.6	4.3
Snap-on Tools Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	0.3	0.4
Provision	0.0	0.0
Usage	(0.2)	(0.1)
Restructuring reserve, ending balance	0.1	0.3
Repair Systems  & Information Group
Restructuring Reserve [Roll Forward]
Restructuring reserve, beginning balance	2.4	3.8
Provision	0.0	0.0
Usage	(1.3)	(1.4)
Restructuring reserve, ending balance	$ 1.1	$ 2.4

X

- Definition

Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-URI https://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 17
-Subparagraph (f)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3367-108585

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X

- Definition

Amount of expenses associated with exit or disposal activities pursuant to an authorized plan. Excludes expenses related to a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 45
-Paragraph 3
-URI https://asc.fasb.org/extlink&oid=109237686&loc=d3e17752-110868

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 5.P.3)
-URI https://asc.fasb.org/extlink&oid=115931487&loc=d3e140864-122747

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(b)(1))
-URI https://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

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X

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-URI https://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b)(2))
-URI https://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

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X

- 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.

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