Segment Information - Company's Segments Information (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Segment Information [Line Items]
Net sales	$ 1,357.8	$ 1,014.6	$ 1,048.5	$ 1,003.1	$ 1,320.6	$ 1,012.4	$ 1,075.9	$ 1,033.2	$ 4,424.0	$ 4,442.1	$ 4,169.8
Earnings (losses) from operations:
Earnings from operations for segments									960.6	1,015.2	990.0
Americas
Segment Information [Line Items]
Net sales									1,924.0	1,960.3	1,870.9
Earnings (losses) from operations:
Earnings from operations for segments									382.2	386.7	399.0
Asia-Pacific
Segment Information [Line Items]
Net sales									1,258.2	1,239.0	1,095.0
Earnings (losses) from operations:
Earnings from operations for segments									254.3	311.5	287.7
Japan
Segment Information [Line Items]
Net sales									649.8	643.0	596.3
Earnings (losses) from operations:
Earnings from operations for segments									229.7	237.2	209.3
Europe
Segment Information [Line Items]
Net sales									498.3	504.4	489.0
Earnings (losses) from operations:
Earnings from operations for segments									83.1	86.2	90.4
Total reportable segments
Segment Information [Line Items]
Net sales									4,330.3	4,346.7	4,051.2
Earnings (losses) from operations:
Earnings from operations for segments									949.3	1,021.6	986.4
Other
Segment Information [Line Items]
Net sales									93.7	95.4	118.6
Earnings (losses) from operations:
Earnings from operations for segments									$ 11.3	$ (6.4)	$ 3.6