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Stock Compensation (Equity-based compensation programs) (Details) (USD $)
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Feb. 28, 2013
2013 Long-Term Incentive Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized 22,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= k_TwoThousandThirteenLongTermIncentivePlanMember
     
Vesting period, years 3 years      
Options granted remaining authorized, but unissued, shares 20,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= k_TwoThousandThirteenLongTermIncentivePlanMember
     
Contractual term, years 10 years      
Shares, Issued       2us-gaap_SharesIssued
/ us-gaap_PlanNameAxis
= k_TwoThousandThirteenLongTermIncentivePlanMember
Shares, Reduced From Remaining Available       1k_SharesReducedFromRemainingAvailable
/ us-gaap_PlanNameAxis
= k_TwoThousandThirteenLongTermIncentivePlanMember
Shares, Reduced From Outstanding Award       1k_SharesReducedFromOutstandingAward
/ us-gaap_PlanNameAxis
= k_TwoThousandThirteenLongTermIncentivePlanMember
2009 Long-Term Incentive Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period, years 3 years      
Contractual term, years 10 years      
2009 Non-Employee Director Stock Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized 500,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= k_TwoThousandNineNonEmployeeDirectorStockPlanMember
     
Number of shares awarded 23,890k_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesAwarded
/ us-gaap_PlanNameAxis
= k_TwoThousandNineNonEmployeeDirectorStockPlanMember
26,504k_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesAwarded
/ us-gaap_PlanNameAxis
= k_TwoThousandNineNonEmployeeDirectorStockPlanMember
26,940k_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesAwarded
/ us-gaap_PlanNameAxis
= k_TwoThousandNineNonEmployeeDirectorStockPlanMember
 
2002 Employee Stock Purchase Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized 400,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
     
Maximum number of shares allowed to be issued under plan 2,500,000k_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesToBeIssued
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
     
Purchase price, percentage of fair market value of stock on last day of quaterly purchase period 95.00%k_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfFairValueOfStockThatEqualsPurchasePrice
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
     
Maximum value of purchases for any employee in any calendar year 25,000k_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumValueOfStockPurchasedFairMarketValue
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
     
Number of shares purchased by employees under plan 75,000k_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPurchasedUnderEmployeePurchasePlan
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
85,000k_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPurchasedUnderEmployeePurchasePlan
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
107,000k_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPurchasedUnderEmployeePurchasePlan
/ us-gaap_PlanNameAxis
= k_TwoThousandTwoEmployeeStockPurchasePlanMember
 
International Subsidiary Employee Stock Purchase Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares purchased by employees under plan 58,000k_SharesPurchasedByEmployees
/ us-gaap_PlanNameAxis
= k_InternationalSubsidiaryEmployeeStockPurchasePlanMember
58,000k_SharesPurchasedByEmployees
/ us-gaap_PlanNameAxis
= k_InternationalSubsidiaryEmployeeStockPurchasePlanMember
71,000k_SharesPurchasedByEmployees
/ us-gaap_PlanNameAxis
= k_InternationalSubsidiaryEmployeeStockPurchasePlanMember
 
Employer Matching Contribution, Percent 100.00%us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent
/ us-gaap_PlanNameAxis
= k_InternationalSubsidiaryEmployeeStockPurchasePlanMember