Quarterly Financial Data (Quarterly Financial Data) (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended																12 Months Ended
	May 31, 2018		Feb. 28, 2018		Nov. 30, 2017		Aug. 31, 2017		May 31, 2017		Feb. 28, 2017		Nov. 30, 2016		Aug. 31, 2016		May 31, 2018		May 31, 2017		May 31, 2016
Quarterly Financial Data [Abstract]
Service revenue	$ 853.4		$ 848.4		$ 812.5		$ 803.1		$ 784.6		$ 782.6		$ 760.0		$ 773.5		$ 3,317.4		$ 3,100.7		$ 2,905.8
Interest on funds held for clients	17.7		18.1		14.0		13.7		14.0		13.2		11.4		12.0		63.5		50.6		46.1
Total revenue	871.1		866.5		826.5		816.8		798.6		795.8		771.4		785.5		3,380.9		3,151.3		2,951.9
Operating income	317.8		292.5		332.2		345.0		298.9		306.6		311.1		323.0		1,287.5		1,239.6		1,146.6
Investment income, net	2.5		2.3		1.7		2.1		1.6		1.2		0.9		1.5		8.6		5.2		4.5
Income before income taxes	320.3		294.8		333.9		347.1		300.5		307.8		312.0		324.5		1,296.1		1,244.8		1,151.1
Income taxes	91.8	[1]	34.4	[1]	116.9	[1]	119.3	[1]	105.2		105.3		109.9		107.1		362.4	[1]	427.5		394.3
Net income	$ 228.5		$ 260.4		$ 217.0		$ 227.8		$ 195.3		$ 202.5		$ 202.1		$ 217.4		$ 933.7		$ 817.3		$ 756.8
Basic earnings per share	$ 0.64	[2]	$ 0.72	[2]	$ 0.60	[2]	$ 0.63	[2]	$ 0.54	[2]	$ 0.56	[2]	$ 0.56	[2]	$ 0.60	[2]	$ 2.60	[2]	$ 2.27	[2]	$ 2.10
Diluted earnings per share	$ 0.63	[2]	$ 0.72	[2]	$ 0.60	[2]	$ 0.63	[2]	$ 0.54	[2]	$ 0.56	[2]	$ 0.56	[2]	$ 0.60	[2]	$ 2.58	[2]	$ 2.25	[2]	$ 2.09
Weighted-average common shares outstanding	359.0		359.2		359.1		358.9		359.3		359.0		360.2		361.0		359.0		359.8		360.7
Weighted-average common shares outstanding, assuming dilution	361.5		362.0		361.4		361.3		362.1		361.8		362.6		364.1		361.5		362.6		362.5
Cash dividends per common share	$ 0.56		$ 0.50		$ 0.50		$ 0.50		$ 0.46		$ 0.46		$ 0.46		$ 0.46		$ 2.06		$ 1.84		$ 1.68
Total net realized gains			$ 0.1	[3]											$ 0.1	[3]	$ 0.1	[3]	$ 0.1	[3]	$ 0.1

[1] As a result of the Tax Act, the effective income tax rate for the three months ended February 28, 2018 was significantly impacted by certain one-time net tax benefits. Refer to Note K for further details.

[2] Each quarter is a discrete period and the sum of the four quarters' basic and diluted earnings per share amounts may not equal the full year amount.

[3] Total net realized gains on the combined funds held for clients and corporate investment portfolios.