Income Taxes - Additional Information (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2019	Jul. 31, 2018	Jul. 31, 2019	Jul. 31, 2018
Discrete tax items [Line Items]
Effective tax rate (percent)	22.30%	20.50%	20.00%	23.00%
Income tax expense (benefit)	$ 39.1	$ 37.3	$ 65.4	$ 85.5
Possible decrease in unrecognized tax benefits	$ 6.0		6.0
Change In Estimated 2018 Foreign Derived Intangible Income
Discrete tax items [Line Items]
Income tax expense (benefit)			$ (7.5)
Effective income tax rate reconciliation, deduction (percent)			(2.30%)
Lapse In Statue Of Limitations
Discrete tax items [Line Items]
Income tax expense (benefit)		$ (8.0)
Effective income tax rate reconciliation, deduction (percent)		(4.40%)		(2.10%)