Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2017	Jul. 31, 2017	Apr. 30, 2017	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Disaggregation of Revenue [Line Items]
Net revenue	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 553.8	$ 515.3	$ 501.8	$ 485.7	$ 2,569.8	$ 2,056.6	$ 2,031.0
Contract with customer, liability, revenue recognized									1,500.0
Indirect
Disaggregation of Revenue [Line Items]
Net revenue									1,830.8	1,443.8	1,468.9
Direct
Disaggregation of Revenue [Line Items]
Net revenue									739.0	612.8	562.1
Americas
Disaggregation of Revenue [Line Items]
Net revenue									1,049.9	871.1	871.9
U.S.
Disaggregation of Revenue [Line Items]
Net revenue									874.6	740.4	742.1
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue									175.3	130.7	129.8
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue									1,034.3	815.4	800.4
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue									485.6	370.1	358.7
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue									1,021.6	787.5	810.4
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue									731.8	561.4	472.7
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue									616.2	528.8	575.2
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue									182.0	152.1	138.8
Other
Disaggregation of Revenue [Line Items]
Net revenue									$ 18.2	$ 26.8	$ 33.9