Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2019	Apr. 30, 2018
Disaggregation of Revenue [Line Items]
Net revenue	$ 735.5	$ 559.9
Contract with customer, liability, revenue recognized	643.4
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	516.4	398.3
Direct
Disaggregation of Revenue [Line Items]
Net revenue	219.1	161.6
Americas
Disaggregation of Revenue [Line Items]
Net revenue	295.8	233.5
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	249.1	195.9
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	46.7	37.6
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	297.2	220.9
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	142.5	105.5
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	304.3	221.8
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	213.2	155.6
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	167.5	135.4
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	45.5	41.8
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 5.0	$ 5.3