Revenue Recognition (Contract Revenue) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2018	Jul. 31, 2017	Jul. 31, 2018	Jul. 31, 2017
Disaggregation of Revenue [Line Items]
Net revenue	$ 611.7	$ 501.8	$ 1,171.6	$ 987.5
Contract with customer, liability, revenue recognized			922.5
Indirect
Disaggregation of Revenue [Line Items]
Net revenue	440.2	354.7	838.5	694.8
Direct
Disaggregation of Revenue [Line Items]
Net revenue	171.5	147.1	333.1	292.7
Americas
Disaggregation of Revenue [Line Items]
Net revenue	247.5	214.0	481.0	424.1
U.S.
Disaggregation of Revenue [Line Items]
Net revenue	205.2	184.6	401.1	364.4
Other Americas
Disaggregation of Revenue [Line Items]
Net revenue	42.3	29.4	79.9	59.7
Europe, Middle East and Africa
Disaggregation of Revenue [Line Items]
Net revenue	248.3	199.3	469.2	389.0
Asia Pacific
Disaggregation of Revenue [Line Items]
Net revenue	115.9	88.5	221.4	174.4
Architecture, Engineering and Construction
Disaggregation of Revenue [Line Items]
Net revenue	243.1	189.6	464.9	375.5
Manufacturing
Disaggregation of Revenue [Line Items]
Net revenue	146.1	132.3	281.5	260.6
AutoCAD and AutoCAD LT
Disaggregation of Revenue [Line Items]
Net revenue	176.6	135.6	332.2	264.6
Media and Entertainment
Disaggregation of Revenue [Line Items]
Net revenue	41.7	38.0	83.5	74.5
Other
Disaggregation of Revenue [Line Items]
Net revenue	$ 4.2	$ 6.3	$ 9.5	$ 12.3