Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Disaggregation of Revenue [Line Items]
Net revenue	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 3,274.3	$ 2,569.8	$ 2,056.6
Indirect
Disaggregation of Revenue [Line Items]
Net revenue									2,282.2	1,830.8	1,443.8
Direct
Disaggregation of Revenue [Line Items]
Net revenue									992.1	739.0	612.8
Americas
Disaggregation of Revenue [Line Items]
Net revenue									1,335.8	1,049.9	871.1
U.S.
Disaggregation of Revenue [Line Items]
Net revenue									1,108.9	874.6	740.4
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue									226.9	175.3	130.7
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue									1,303.5	1,034.3	815.4
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue									635.0	485.6	370.1
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue									1,377.1	1,021.6	787.5
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue									726.1	616.2	528.8
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue									948.2	731.8	561.4
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue									199.2	182.0	152.1
Other
Disaggregation of Revenue [Line Items]
Net revenue									$ 23.7	$ 18.2	$ 26.8