Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2019	Jul. 31, 2018	Jul. 31, 2019	Jul. 31, 2018
Disaggregation of Revenue [Line Items]
Net revenue	$ 796.8	$ 611.7	$ 1,532.3	$ 1,171.6
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	560.2	440.2	1,076.6	838.5
Direct
Disaggregation of Revenue [Line Items]
Net revenue	236.6	171.5	455.7	333.1
Americas
Disaggregation of Revenue [Line Items]
Net revenue	325.9	247.5	621.7	481.0
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	267.9	205.2	517.0	401.1
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	58.0	42.3	104.7	79.9
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	316.2	248.3	613.4	469.2
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	154.7	115.9	297.2	221.4
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	334.2	243.1	638.5	464.9
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	231.3	176.6	444.5	332.2
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	174.6	146.1	342.1	281.5
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	50.8	41.7	96.3	83.5
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 5.9	$ 4.2	$ 10.9	$ 9.5