Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2020	Apr. 30, 2019
Disaggregation of Revenue [Line Items]
Net revenue	$ 885.7	$ 735.5
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	623.4	516.4
Direct
Disaggregation of Revenue [Line Items]
Net revenue	262.3	219.1
Americas
Disaggregation of Revenue [Line Items]
Net revenue	362.2	295.8
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	300.6	249.1
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	61.6	46.7
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	344.8	297.2
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	178.7	142.5
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	382.7	304.3
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	262.2	213.2
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	182.9	167.5
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	52.6	45.5
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 5.3	$ 5.0