Retirement Benefit Plans - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Defined Contribution Plan Disclosure [Line Items]
Projected benefit obligation of plan assets	$ 110.0	$ 103.5
Accumulated benefit obligation	105.2	97.3
Fair value of plan assets	107.2	96.2
Other long-term liabilities	12.1	11.6
Net periodic (benefit) cost	2.8	3.7	$ (3.1)
Estimated future employer contributions in next fiscal year	$ 5.5
United States
Defined Contribution Plan Disclosure [Line Items]
Maximum annual contributions per employee	75.00%
Cost Recognized	$ 21.6	21.4	17.1
Foreign Plan
Defined Contribution Plan Disclosure [Line Items]
Contributions paid by employer	$ 31.7	$ 28.7	$ 29.6
Mandatory Retirement Savings, Cash Balance Plan
Defined Contribution Plan Disclosure [Line Items]
Weighted-average interest crediting rate	1.00%	1.00%	1.00%
Supplementary Retirement Savings, Cash Balance Plan
Defined Contribution Plan Disclosure [Line Items]
Weighted-average interest crediting rate	0.10%	0.10%	0.30%