Segment Information - Products and Services (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Net Sales from External Customer [Line Items]
Net sales	$ 4,074.8	$ 4,373.2	$ 4,186.1	$ 3,606.4	$ 3,752.1	$ 3,933.2	$ 3,891.7	$ 3,256.0	$ 16,240.5	$ 14,832.9	$ 13,672.7
Percentage of Total Net Sales									100.00%	100.00%	100.00%
Total Hardware
Net Sales from External Customer [Line Items]
Net sales									$ 13,082.4	$ 11,960.4	$ 10,916.0
Percentage of Total Net Sales									80.60%	80.60%	79.80%
Notebooks/Mobile Devices
Net Sales from External Customer [Line Items]
Net sales									$ 4,053.6	$ 3,519.8	$ 2,942.9
Percentage of Total Net Sales									25.00%	23.70%	21.50%
Netcomm Products
Net Sales from External Customer [Line Items]
Net sales									$ 2,119.8	$ 2,040.3	$ 1,957.0
Percentage of Total Net Sales									13.10%	13.80%	14.30%
Desktops
Net Sales from External Customer [Line Items]
Net sales									$ 1,318.2	$ 1,207.0	$ 1,087.7
Percentage of Total Net Sales									8.10%	8.10%	8.00%
Video
Net Sales from External Customer [Line Items]
Net sales									$ 1,185.6	$ 1,078.4	$ 963.0
Percentage of Total Net Sales									7.30%	7.30%	7.00%
Enterprise and Data Storage (Including Drives)
Net Sales from External Customer [Line Items]
Net sales									$ 1,099.2	$ 1,087.3	$ 1,073.9
Percentage of Total Net Sales									6.80%	7.30%	7.90%
Other Hardware
Net Sales from External Customer [Line Items]
Net sales									$ 3,306.0	$ 3,027.6	$ 2,891.5
Percentage of Total Net Sales									20.30%	20.40%	21.10%
Software
Net Sales from External Customer [Line Items]
Net sales									$ 2,347.0	$ 2,156.9	$ 2,072.3
Percentage of Total Net Sales									14.40%	14.50%	15.20%
Services
Net Sales from External Customer [Line Items]
Net sales									$ 697.3	$ 602.7	$ 564.2
Percentage of Total Net Sales									4.30%	4.10%	4.10%
Other
Net Sales from External Customer [Line Items]
Net sales									$ 113.8	$ 112.9	$ 120.2
Percentage of Total Net Sales									0.70%	0.80%	0.90%