Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2020	Oct. 31, 2019	Oct. 31, 2020	Oct. 31, 2019
Disaggregation of Revenue [Line Items]
Net revenue	$ 952.4	$ 842.7	$ 2,751.2	$ 2,375.0
Design
Disaggregation of Revenue [Line Items]
Net revenue	847.7	748.3	2,466.8	2,126.4
Make
Disaggregation of Revenue [Line Items]
Net revenue	76.5	57.9	214.9	154.8
Other
Disaggregation of Revenue [Line Items]
Net revenue	28.2	36.5	69.5	93.8
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	656.2	586.6	1,918.9	1,663.2
Direct
Disaggregation of Revenue [Line Items]
Net revenue	296.2	256.1	832.3	711.8
Americas
Disaggregation of Revenue [Line Items]
Net revenue	392.9	349.3	1,126.6	971.0
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	328.5	287.3	938.6	804.3
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	64.4	62.0	188.0	166.7
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	364.3	329.6	1,063.8	943.0
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	195.2	163.8	560.8	461.0
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	419.4	358.0	1,199.1	996.5
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	278.8	245.4	812.9	689.9
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	194.1	182.2	562.5	524.3
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	54.0	50.6	159.9	146.9
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 6.1	$ 6.5	$ 16.8	$ 17.4