Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2018	Apr. 30, 2017
Disaggregation of Revenue [Line Items]
Net revenue	$ 559.9	$ 485.7
Americas
Disaggregation of Revenue [Line Items]
Net revenue	233.5	210.1
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	195.9	179.8
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	37.6	30.3
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	220.9	189.7
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	105.5	85.9
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	221.8	185.9
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	135.4	128.3
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	155.6	129.0
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	41.8	36.5
Other
Disaggregation of Revenue [Line Items]
Net revenue	5.3	6.0
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	398.3	340.1
Direct
Disaggregation of Revenue [Line Items]
Net revenue	$ 161.6	$ 145.6