Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2018	Oct. 31, 2017	Oct. 31, 2018	Oct. 31, 2017
Disaggregation of Revenue [Line Items]
Net revenue	$ 660.9	$ 515.3	$ 1,832.5	$ 1,502.8
Contract with customer, liability, revenue recognized			1,260.0
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	477.0	360.6	1,315.5	1,055.4
Direct
Disaggregation of Revenue [Line Items]
Net revenue	183.9	154.7	517.0	447.4
Americas
Disaggregation of Revenue [Line Items]
Net revenue	268.5	214.6	749.5	638.7
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	225.0	182.4	626.1	546.8
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	43.5	32.2	123.4	91.9
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	266.5	205.4	735.7	594.4
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	125.9	95.3	347.3	269.7
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	263.8	195.4	728.7	570.9
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	190.6	142.7	522.8	407.3
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	158.5	132.0	440.0	392.6
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	43.6	37.7	127.1	112.2
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 4.4	$ 7.5	$ 13.9	$ 19.8