Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2019	Oct. 31, 2018
Disaggregation of Revenue [Line Items]
Net revenue	$ 842.7	$ 660.9	$ 2,375.0	$ 1,832.5
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	586.6	477.0	1,663.2	1,315.5
Direct
Disaggregation of Revenue [Line Items]
Net revenue	256.1	183.9	711.8	517.0
Americas
Disaggregation of Revenue [Line Items]
Net revenue	349.3	268.5	971.0	749.5
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	287.3	225.0	804.3	626.1
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	62.0	43.5	166.7	123.4
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	329.6	266.5	943.0	735.7
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	163.8	125.9	461.0	347.3
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	358.0	263.8	996.5	728.7
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	245.4	190.6	689.9	522.8
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	182.2	158.5	524.3	440.0
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	50.6	43.6	146.9	127.1
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 6.5	$ 4.4	$ 17.4	$ 13.9