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Stock-Based Compensation and Other Stock Plans - Summary of Changes in Non-Vested Awards (Detail) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Nonvested Performance Shares [Member]    
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]    
Shares, at beginning of year 381,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Shares, Granted 177,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Shares, Vested (225,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Shares, Cancellations (6,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Shares, at end of year 327,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Fair Value Price per Share, at beginning of year $ 68.13us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Fair Value Price per Share, Granted $ 102.11us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Fair Value Price per Share, Vested $ 60.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Fair Value Price per Share, Cancellations $ 78.65us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Fair Value Price per Share, at end of year $ 91.92us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_NonvestedPerformanceSharesMember
 
Cash-Settled Stock Appreciation Rights [Member]    
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]    
Shares, at beginning of year 126,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Shares, Granted 4,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Shares, Vested (81,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Shares, Cancellations (2,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Shares, at end of year 47,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Fair Value Price per Share, at beginning of year $ 43.72us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Fair Value Price per Share, Granted $ 32.86us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Fair Value Price per Share, Vested $ 73.25us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Fair Value Price per Share, at end of year $ 68.35us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Stock-Settled SARs [Member]    
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]    
Shares, at beginning of year 122,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Shares, Granted 116,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Shares, Exercised (3,000)sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisedInPeriod
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Shares, Cancellations (12,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Shares, at end of year 223,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
122,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
Shares, Exercisable at end of year 29,000sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNonvestedNumber
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Exercise Price per Share, Outstanding at beginning of year $ 79.29sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Fair Value Price per Share, Granted $ 19.55us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
$ 17.47us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
Exercise Price per Share, Granted $ 109.98sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageExercisedPrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Exercise Price per Share, Exercised $ 79.04sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisedInPeriodWeightedAverageExercisedPrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Exercise Price per Share, Forfeited or expired $ 80.97sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriodWeightedAverageExercisedPrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Exercise Price per Share, Outstanding at end of year $ 94.90sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
$ 79.29sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
Exercise Price per Share, Exercisable at end of year $ 79.40sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNonvestedWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Remaining Contractual Term, Outstanding at end of year 8 years 7 months 6 days  
Remaining Contractual Term, Exercisable at end of year 8 years 1 month 6 days  
Aggregate Intrinsic Value, Outstanding at end of year $ 9.2sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedIntrinsicValues
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember
 
Aggregate Intrinsic Value, Exercisable at end of year $ 1.6sna_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNonvestedIntrinsicValues
/ us-gaap_AwardTypeAxis
= sna_StockSettledStockAppreciationRightsMember