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Income Taxes (Narrative) (Detail) (USD $)
In Millions, unless otherwise specified
3 Months Ended
Apr. 03, 2015
Apr. 04, 2014
Jan. 02, 2015
Income Tax Contingency [Line Items]      
Effective income tax rate 23.00%us-gaap_EffectiveIncomeTaxRateContinuingOperations 23.00%us-gaap_EffectiveIncomeTaxRateContinuingOperations  
Statutory federal income tax rate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate  
Unrecognized tax benefits that would impact effective tax rate $ 43.7us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate   $ 45.6us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate
Unrecognized tax benefit liabilities include interest and penalties 5.2us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued   4.7us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued
Tax Year 2010 and 2011 [Member] | Internal Revenue Service (IRS) [Member]      
Income Tax Contingency [Line Items]      
Proposed Adjustments on Income Tax Assessments $ 67.0us-gaap_IncomeTaxExaminationEstimateOfPossibleLoss
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_InternalRevenueServiceIRSMember
/ us-gaap_TaxPeriodAxis
= trmb_TaxYear2010and2011Member