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Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill by Segment (Details) $ in Millions	9 Months Ended
	Oct. 02, 2021 USD ($)
Goodwill [Roll Forward]
Balance as of January 2, 2021	$ 982.4
Currency translation	(20.6)
Acquisitions and related adjustments	209.2
Balance as of October 2, 2021	1,171.0
Commercial & Industrial Group
Goodwill [Roll Forward]
Balance as of January 2, 2021	331.2
Currency translation	(12.6)
Acquisitions and related adjustments	14.0
Balance as of October 2, 2021	332.6
Snap-on Tools Group
Goodwill [Roll Forward]
Balance as of January 2, 2021	12.4
Currency translation	0.0
Acquisitions and related adjustments	0.0
Balance as of October 2, 2021	12.4
Repair Systems & Information Group
Goodwill [Roll Forward]
Balance as of January 2, 2021	638.8
Currency translation	(8.0)
Acquisitions and related adjustments	195.2
Balance as of October 2, 2021	$ 826.0

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- Definition

Goodwill acquired and related adjustment.

+ References

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- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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Amount of foreign currency translation gain (loss) which increases (decreases) an asset representing future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

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