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Employee Stock Benefit Plans (Narrative) (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Jan. 02, 2015
Jan. 03, 2014
Dec. 28, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 3 years 9 months 12 days    
Options to purchase, number of shares outstanding 13,135,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber 14,943,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber  
Number of restricted stock units unvested 3,054,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber 1,966,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber  
Shares available for future grant 14,376,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant    
Weighted average grant-date fair value, granted $ 30.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue    
Exercise prices for options outstanding, lower limit $ 5.06us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeLowerRangeLimit    
Exercise prices for options outstanding, upper limit $ 35.02us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit    
Closing stock price $ 26.91trmb_ShareBasedCompensationArrangementByShareBasedPaymentAwardClosingStockPriceOfOptionsExercised    
Total intrinsic value of options exercised $ 61.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue $ 55.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue $ 89.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
Total unamortized compensation expense 37.3us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized    
Total unamortized compensation expense weighted-average recognition period, in years 2 years 5 months 28 days    
Minimum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share units granted vesting period, in years 4 years    
Maximum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share units granted vesting period, in years 5 years    
Stock Plan Assumed Through Acquisition [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock plan acquired 1trmb_EmployeeStockBenefitPlanPlanAssumedThroughAcquisition
/ us-gaap_PlanNameAxis
= trmb_StockPlanAssumedThroughAcquisitionMember
   
Options to purchase, number of shares outstanding 95,639us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_PlanNameAxis
= trmb_StockPlanAssumedThroughAcquisitionMember
   
1990 Stock Option Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Shares available for future grant 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= trmb_NineteenNinetyStockOptionPlanMember
   
Employee Stock Purchase Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Percentage of lower fair market value to be purchased of common stock through payroll deductions 85.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardDiscountFromMarketPricePurchaseDate
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
   
Shares issued 666,995us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
636,227us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
702,622us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
Stock-based compensation expense 4.7us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
4.0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
3.9us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
Maximum number of shares authorized for grant 39,100,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
   
Employee stock options granted term, in months 6 months    
Shares available for future grant 11,915,528us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
   
Weighted average grant-date fair value, granted $ 8.32us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
$ 8.05us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
$ 6.27us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_PlanNameAxis
= trmb_EmployeeStockPurchasePlanMember
Two Thousand Two Stock Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Maximum number of shares authorized for grant 62,570,248us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
Percentage of fair market value of Common Stock 100.00%trmb_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodExercisePriceBasedOnPercentageOfFairMarketValueOfCommonStock
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
2002 Stock Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Shares available for future grant 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= trmb_A1993StockPlanMember
   
1992 Employee Stock Bonus Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Options to purchase, number of shares outstanding 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_PlanNameAxis
= trmb_NineteenNinetyTwoEmployeeStockBonusPlanMember
   
Shares available for future grant 3,271us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= trmb_NineteenNinetyTwoEmployeeStockBonusPlanMember
   
Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock-based compensation expense 19.0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
12.2us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
8.6us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Share units granted vesting period, in years 3 years    
Total unamortized compensation expense 53.5us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
   
Total unamortized compensation expense weighted-average recognition period, in years 2 years 3 months 11 days    
Restricted Stock Units (RSUs) [Member] | Two Thousand Two Stock Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share units granted vesting percentage 100.00%trmb_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodPercentageOfSharesVested
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
Options to purchase, number of shares outstanding 13,039,205us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
Number of restricted stock units unvested 3,053,873us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
Shares available for future grant 14,372,588us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
   
Share units granted vesting period, in years 3 years    
Employee Stock Option [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted average grant-date fair value of stock options granted $ 9.07us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 7.90us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 7.51us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Stock-based compensation expense $ 19.7us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 20.2us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
$ 20.3us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_EmployeeStockOptionMember
Non-Employee Director Stock Options [Member] | Two Thousand Two Stock Plan [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock options granted vesting rate 1/12th per month    
Share units granted vesting period, in years 1 year    
Non-Employee Director Stock Options [Member] | Two Thousand Two Stock Plan [Member] | Minimum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 84 months    
Non-Employee Director Stock Options [Member] | Two Thousand Two Stock Plan [Member] | Maximum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 120 months    
Stock Option Granted Prior To 2013 [Member] | Two Thousand Two Stock Plan [Member] | First Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 20.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGrantedPriorTo2013Member
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FirstAnniversaryMember
   
Stock Option Granted Prior To 2013 [Member] | Two Thousand Two Stock Plan [Member] | Fifth Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 20.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGrantedPriorTo2013Member
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FifthAnniversaryMember
   
Stock Option Granted Prior To 2013 [Member] | Two Thousand Two Stock Plan [Member] | Minimum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 84 months    
Stock Option Granted Prior To 2013 [Member] | Two Thousand Two Stock Plan [Member] | Maximum [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 120 months    
Stock Option Granted Prior to 2013 Certain Grants [Member] | Two Thousand Two Stock Plan [Member] | Second Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 40.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGrantedPriorto2013CertainGrantsMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_SecondAnniversaryMember
   
Stock Option Granted Prior to 2013 Certain Grants [Member] | Two Thousand Two Stock Plan [Member] | Fifth Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 20.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGrantedPriorto2013CertainGrantsMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FifthAnniversaryMember
   
Stock Option Granted 2013 And After [Member] | Two Thousand Two Stock Plan [Member] | First Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 25.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGranted2013AndAfterMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FirstAnniversaryMember
   
Stock Option Granted 2013 And After [Member] | Two Thousand Two Stock Plan [Member] | Fourth Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 25.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_StockOptionGranted2013AndAfterMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FourthAnniversaryMember
   
Certain Stock Option Grants [Member] | Two Thousand Two Stock Plan [Member] | Second Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 50.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_CertainStockOptionGrantsMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_SecondAnniversaryMember
   
Certain Stock Option Grants [Member] | Two Thousand Two Stock Plan [Member] | Fourth Anniversary [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 25.00%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= trmb_CertainStockOptionGrantsMember
/ us-gaap_PlanNameAxis
= trmb_TwoThousandTwoStockPlanMember
/ us-gaap_VestingAxis
= trmb_FourthAnniversaryMember