Revenues (Disaggregation of revenue) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 03, 2020	Dec. 28, 2018
Disaggregation of Revenue [Line Items]
Revenues	$ 10,976	$ 10,194
United States
Disaggregation of Revenue [Line Items]
Revenues	10,100	9,265
International
Disaggregation of Revenue [Line Items]
Revenues	876	929
Cost-reimbursement and fixed-price-incentive-fee
Disaggregation of Revenue [Line Items]
Revenues	5,928	5,469
Firm-fixed-price
Disaggregation of Revenue [Line Items]
Revenues	3,574	3,169
Time-and-materials and fixed-price-level-of-effort
Disaggregation of Revenue [Line Items]
Revenues	1,474	1,556
DoD and U.S. Intelligence Community
Disaggregation of Revenue [Line Items]
Revenues	5,325	4,873
Other government agencies
Disaggregation of Revenue [Line Items]
Revenues	4,308	3,841
Commercial and non-U.S. customers
Disaggregation of Revenue [Line Items]
Revenues	1,343	1,480
Defense Solutions
Disaggregation of Revenue [Line Items]
Revenues, reclassified amount		41
Revenues	5,366	4,966
Defense Solutions | United States
Disaggregation of Revenue [Line Items]
Revenues	4,995	4,586
Defense Solutions | International
Disaggregation of Revenue [Line Items]
Revenues	371	380
Defense Solutions | Cost-reimbursement and fixed-price-incentive-fee
Disaggregation of Revenue [Line Items]
Revenues	3,697	3,420
Defense Solutions | Firm-fixed-price
Disaggregation of Revenue [Line Items]
Revenues	1,203	1,051
Defense Solutions | Time-and-materials and fixed-price-level-of-effort
Disaggregation of Revenue [Line Items]
Revenues	466	495
Defense Solutions | DoD and U.S. Intelligence Community
Disaggregation of Revenue [Line Items]
Revenues	4,660	4,359
Defense Solutions | Other government agencies
Disaggregation of Revenue [Line Items]
Revenues	295	185
Defense Solutions | Commercial and non-U.S. customers
Disaggregation of Revenue [Line Items]
Revenues	411	422
Civil
Disaggregation of Revenue [Line Items]
Revenues	3,636	3,411
Civil | United States
Disaggregation of Revenue [Line Items]
Revenues	3,131	2,862
Civil | International
Disaggregation of Revenue [Line Items]
Revenues	505	549
Civil | Cost-reimbursement and fixed-price-incentive-fee
Disaggregation of Revenue [Line Items]
Revenues	1,997	1,860
Civil | Firm-fixed-price
Disaggregation of Revenue [Line Items]
Revenues	1,075	984
Civil | Time-and-materials and fixed-price-level-of-effort
Disaggregation of Revenue [Line Items]
Revenues	564	567
Civil | DoD and U.S. Intelligence Community
Disaggregation of Revenue [Line Items]
Revenues	174	128
Civil | Other government agencies
Disaggregation of Revenue [Line Items]
Revenues	2,681	2,380
Civil | Commercial and non-U.S. customers
Disaggregation of Revenue [Line Items]
Revenues	781	903
Health
Disaggregation of Revenue [Line Items]
Revenues	1,974	1,817
Health | United States
Disaggregation of Revenue [Line Items]
Revenues	1,974	1,817
Health | International
Disaggregation of Revenue [Line Items]
Revenues	0	0
Health | Cost-reimbursement and fixed-price-incentive-fee
Disaggregation of Revenue [Line Items]
Revenues	234	189
Health | Firm-fixed-price
Disaggregation of Revenue [Line Items]
Revenues	1,296	1,134
Health | Time-and-materials and fixed-price-level-of-effort
Disaggregation of Revenue [Line Items]
Revenues	444	494
Health | DoD and U.S. Intelligence Community
Disaggregation of Revenue [Line Items]
Revenues	491	386
Health | Other government agencies
Disaggregation of Revenue [Line Items]
Revenues	1,332	1,276
Health | Commercial and non-U.S. customers
Disaggregation of Revenue [Line Items]
Revenues	$ 151	$ 155