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Multiemployer Pension And Postretirement Plans (Multiemplyer Pension Plans Trust Funds) (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Multiemployer Plans [Line Items]      
Multiemployer Plan, company contributions $ 14.7us-gaap_MultiemployerPlanPeriodContributions $ 14.5us-gaap_MultiemployerPlanPeriodContributions $ 13.5us-gaap_MultiemployerPlanPeriodContributions
Bakery and Confectionary Union and Industry International Pension Fund [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 526118572 [1]    
Multiemployer Plan Number 001 [1]    
Multiemployer Plans, Certified Zone Status Red [1] Red [1]  
Multiemployer Plans, Certified Zone Status Date Dec. 31, 2014 [1] Dec. 31, 2013 [1]  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan Implemented [1]    
Multiemployer Plan, company contributions 5.4us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_BakeryAndConfectionaryUnionAndIndustryInternationalPensionFundMember
[1] 5.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_BakeryAndConfectionaryUnionAndIndustryInternationalPensionFundMember
[1] 4.8us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_BakeryAndConfectionaryUnionAndIndustryInternationalPensionFundMember
[1]
Multiemployer Plans, Surcharge Yes [1]    
Multiemployer Plans, collective bargaining arrangement first expiration date Oct. 31, 2015 [1]    
Multiemployer Plans, collective bargaining arrangement last expiration date Apr. 30, 2017 [1]    
Multiemployer Plans, collective bargaining arrangement expiration date Apr. 30, 2017 [1]    
Bakery and Confectionary Union and Industry International Pension Fund [Member] | CBA Expiring 2017      
Multiemployer Plans [Line Items]      
Multiemployer Plans, percentage of employees covered by single collective bargaining arrangement 70.00%us-gaap_MultiemployerPlansCollectiveBargainingArrangementPercentageOfEmployersParticipants
/ us-gaap_CollectiveBargainingArrangementAxis
= k_CbaExpiringTwentySeventeenMember
/ us-gaap_MultiemployerPlanNameAxis
= k_BakeryAndConfectionaryUnionAndIndustryInternationalPensionFundMember
[1]    
Central States, Southeast and Southwest Areas Pension Fund [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 366044243 [2]    
Multiemployer Plan Number 001 [2]    
Multiemployer Plans, Certified Zone Status Red [2] Red [2]  
Multiemployer Plans, Certified Zone Status Date Dec. 31, 2014 [2] Dec. 31, 2013 [2]  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan Implemented [2]    
Multiemployer Plan, company contributions 4.5us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_CentralStatesSoutheastAndSouthwestAreasPensionFundMember
[2] 4.5us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_CentralStatesSoutheastAndSouthwestAreasPensionFundMember
[2] 4.3us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_CentralStatesSoutheastAndSouthwestAreasPensionFundMember
[2]
Multiemployer Plans, Surcharge Yes [2]    
Multiemployer Plans, collective bargaining arrangement first expiration date Jan. 31, 2015 [2]    
Multiemployer Plans, collective bargaining arrangement last expiration date Oct. 31, 2017 [2]    
Multiemployer Plans, collective bargaining arrangement expiration date Jul. 27, 2017 [2]    
Multiemployer Plans, percentage of employees covered by single collective bargaining arrangement 40.00%us-gaap_MultiemployerPlansCollectiveBargainingArrangementPercentageOfEmployersParticipants
/ us-gaap_MultiemployerPlanNameAxis
= k_CentralStatesSoutheastAndSouthwestAreasPensionFundMember
[2]    
Western Conference of Teamsters Pension Trust [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 916145047 [3]    
Multiemployer Plan Number 001 [3]    
Multiemployer Plans, Certified Zone Status Green [3] Green [3]  
Multiemployer Plans, Certified Zone Status Date Dec. 31, 2014 [3] Dec. 31, 2013 [3]  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan NA [3]    
Multiemployer Plan, company contributions 1.6us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_WesternConferenceOfTeamstersPensionTrustMember
[3] 1.5us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_WesternConferenceOfTeamstersPensionTrustMember
[3] 1.3us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_WesternConferenceOfTeamstersPensionTrustMember
[3]
Multiemployer Plans, Surcharge No [3]    
Multiemployer Plans, collective bargaining arrangement first expiration date Jan. 31, 2015 [3]    
Multiemployer Plans, collective bargaining arrangement last expiration date Mar. 29, 2018 [3]    
Multiemployer Plans, collective bargaining arrangement expiration date Mar. 24, 2018 [3]    
Multiemployer Plans, percentage of employees covered by single collective bargaining arrangement 40.00%us-gaap_MultiemployerPlansCollectiveBargainingArrangementPercentageOfEmployersParticipants
/ us-gaap_MultiemployerPlanNameAxis
= k_WesternConferenceOfTeamstersPensionTrustMember
[3]    
Hagerstown Motor Carriers and Teamsters Pension Fund [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 526045424    
Multiemployer Plan Number 001    
Multiemployer Plans, Certified Zone Status Red Red  
Multiemployer Plans, Certified Zone Status Date Jun. 30, 2015 Jun. 30, 2014  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan Implemented    
Multiemployer Plan, company contributions 0.5us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_HagerstownMotorCarriersAndTeamstersPensionFundMember
0.5us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_HagerstownMotorCarriersAndTeamstersPensionFundMember
0.4us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_HagerstownMotorCarriersAndTeamstersPensionFundMember
Multiemployer Plans, Surcharge No    
Multiemployer Plans, collective bargaining arrangement expiration date Oct. 03, 2015    
Local 734 Pension Plan [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 516040136    
Multiemployer Plan Number 001    
Multiemployer Plans, Certified Zone Status Red Red  
Multiemployer Plans, Certified Zone Status Date Apr. 30, 2015 Apr. 30, 2014  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan Implemented    
Multiemployer Plan, company contributions 0.3us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_Local734PensionPlanMember
0.3us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_Local734PensionPlanMember
0.3us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_Local734PensionPlanMember
Multiemployer Plans, Surcharge Yes    
Multiemployer Plans, collective bargaining arrangement expiration date Apr. 01, 2015    
Twin Cities Bakery Drivers Pension Plan [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 416172265    
Multiemployer Plan Number 001    
Multiemployer Plans, Certified Zone Status Green Red  
Multiemployer Plans, Certified Zone Status Date Dec. 31, 2014 Dec. 31, 2013  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan NA    
Multiemployer Plan, company contributions 0.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_TwinCitiesBakeryDriversPensionPlanMember
0.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_TwinCitiesBakeryDriversPensionPlanMember
0.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_TwinCitiesBakeryDriversPensionPlanMember
Multiemployer Plans, Surcharge Yes    
Multiemployer Plans, collective bargaining arrangement expiration date May 31, 2015    
Upstate New York Bakery Drivers and Industry Pension Fund [Member]      
Multiemployer Plans [Line Items]      
Entity Tax Identification Number 150612437    
Multiemployer Plan Number 001    
Multiemployer Plans, Certified Zone Status Green Green  
Multiemployer Plans, Certified Zone Status Date Jun. 30, 2014 Jun. 30, 2013  
Multiemployer Plans, Funding Improvement Plan and Rehabilitation Plan NA    
Multiemployer Plan, company contributions 0.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_UpstateNewYorkBakeryDriversAndIndustryPensionFundMember
0.1us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_UpstateNewYorkBakeryDriversAndIndustryPensionFundMember
0.1us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_UpstateNewYorkBakeryDriversAndIndustryPensionFundMember
Multiemployer Plans, Surcharge No    
Multiemployer Plans, collective bargaining arrangement expiration date Sep. 10, 2017    
Other Plans [Member]      
Multiemployer Plans [Line Items]      
Multiemployer Plan, company contributions $ 2.0us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_OtherPlansMember
$ 2.2us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_OtherPlansMember
$ 2.1us-gaap_MultiemployerPlanPeriodContributions
/ us-gaap_MultiemployerPlanNameAxis
= k_OtherPlansMember
[1] The Company is party to multiple CBAs requiring contributions to this fund, each with its own expiration date. Over 70 percent of the Company's participants in this fund are covered by a single CBA that expires on 4/30/2017.
[2] The Company is party to multiple CBAs requiring contributions to this fund, each with its own expiration date. Over 40 percent of the Company's participants in this fund are covered by a single CBA that expires on 7/27/2017.
[3] The Company is party to multiple CBAs requiring contributions to this fund, each with its own expiration date. Over 40 percent of the Company's participants in this fund are covered by a single CBA that expires on 3/24/2018.