Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2020	Jul. 31, 2019	Jul. 31, 2020	Jul. 31, 2019
Disaggregation of Revenue [Line Items]
Net revenue	$ 913.1	$ 796.8	$ 1,798.8	$ 1,532.3
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	639.3	560.2	1,262.7	1,076.6
Direct
Disaggregation of Revenue [Line Items]
Net revenue	273.8	236.6	536.1	455.7
Americas
Disaggregation of Revenue [Line Items]
Net revenue	371.5	325.9	733.7	621.7
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	309.5	267.9	610.1	517.0
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	62.0	58.0	123.6	104.7
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	354.7	316.2	699.5	613.4
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	186.9	154.7	365.6	297.2
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	397.0	334.2	779.7	638.5
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	271.9	231.3	534.1	444.5
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	185.5	174.6	368.4	342.1
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	53.3	50.8	105.9	96.3
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 5.4	$ 5.9	$ 10.7	$ 10.9