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Income Taxes (Narrative) (Details) (USD $)
12 Months Ended
Jan. 02, 2015
Jan. 03, 2014
Dec. 28, 2012
Dec. 30, 2011
Jan. 04, 2014
Dec. 30, 2013
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Unrecognized Tax Benefits that Would Impact Effective Tax Rate $ 45,600,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate $ 38,100,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate        
Tax Credit Carryforward, Expiration Date Jan. 01, 2030          
Foreign subsidiary accumulated undistributed earnings 688,800,000us-gaap_DeferredTaxLiabilitiesUndistributedForeignEarnings          
Unrecognized deferred tax liability 216,800,000us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityUndistributedEarningsOfForeignSubsidiaries          
Total amount of the unrecognized tax benefits 51,389,000us-gaap_UnrecognizedTaxBenefits 44,107,000us-gaap_UnrecognizedTaxBenefits 32,250,000us-gaap_UnrecognizedTaxBenefits 25,984,000us-gaap_UnrecognizedTaxBenefits    
Unrecognized Tax Benefits, Income Tax Penalties and Interest Accrued 4,700,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued 3,600,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued        
Federal [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Net operating loss carryforwards 26,100,000us-gaap_OperatingLossCarryforwards
/ trmb_IncomeTaxesAxis
= trmb_FederalMember
         
Research and development credit carryforwards 600,000us-gaap_TaxCreditCarryforwardAmount
/ trmb_IncomeTaxesAxis
= trmb_FederalMember
         
Federal [Member] | Minimum [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Net operating loss carryforwards, expiration, year Jan. 01, 2025          
Federal [Member] | Maximum [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Net operating loss carryforwards, expiration, year Jan. 01, 2029          
California [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Net operating loss carryforwards 6,800,000us-gaap_OperatingLossCarryforwards
/ trmb_IncomeTaxesAxis
= trmb_CaliforniaMember
         
Research and development credit carryforwards 17,400,000us-gaap_TaxCreditCarryforwardAmount
/ trmb_IncomeTaxesAxis
= trmb_CaliforniaMember
         
Foreign [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Net operating loss carryforwards $ 122,700,000us-gaap_OperatingLossCarryforwards
/ trmb_IncomeTaxesAxis
= trmb_ForeignMember
         
Finland [Member]            
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]            
Enacted Statutory Tax Rate, Percent         20.00%trmb_EnactedStatutoryTaxRatePercent
/ us-gaap_StatementGeographicalAxis
= country_FI
24.50%trmb_EnactedStatutoryTaxRatePercent
/ us-gaap_StatementGeographicalAxis
= country_FI