Segment and Geographic Information - Reportable Segments (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Segment Reporting Information [Line Items]
Total revenues	$ 66,036.0	$ 42,534.2	$ 54,139.6
Operating revenues:	2,107.4	1,673.1	1,308.3
Net operating revenues (loss):	1,475.9	1,150.0	868.0
Net contribution:	1,121.9	868.7	639.5
Segment income:	675.7	506.2	395.1
Net costs not allocated to operating segments	(398.5)	(355.5)	(270.3)
Gain on acquisitions and other gains, net	0.0	3.4	81.9
Income from operations, before tax	277.2	154.1	206.7
Total assets:	19,859.6	18,839.6	13,474.9
Corporate Unallocated
Segment Reporting Information [Line Items]
Total revenues	7.8	1.7	14.6
Operating revenues:	7.8	1.7	14.6
Net operating revenues (loss):	(59.5)	(54.8)	(24.5)
Total assets:	746.3	841.7	418.7
Eliminations
Segment Reporting Information [Line Items]
Total revenues	(23.0)	(17.1)	(19.3)
Operating revenues:	(23.0)	(17.1)	(19.3)
Commercial
Segment Reporting Information [Line Items]
Net contribution:	415.3	299.7	242.2
Segment income:	288.3	192.2	141.9
Commercial | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	63,743.2	39,884.0	52,970.1
Operating revenues:	692.1	534.8	431.5
Net operating revenues (loss):	586.5	433.1	353.4
Total assets:	5,931.0	3,969.9	2,753.6
Institutional
Segment Reporting Information [Line Items]
Net contribution:	295.1	260.9	248.9
Segment income:	174.6	167.7	152.9
Institutional | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	831.8	668.4	624.1
Operating revenues:	831.8	668.4	624.1
Net operating revenues (loss):	483.5	419.4	363.8
Total assets:	11,687.1	12,403.3	8,740.8
Retail
Segment Reporting Information [Line Items]
Net contribution:	280.3	204.4	58.8
Segment income:	115.4	67.8	31.7
Retail | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	1,304.2	1,859.9	432.7
Operating revenues:	426.7	348.0	140.0
Net operating revenues (loss):	302.9	222.4	63.8
Total assets:	971.2	1,380.9	1,245.9
Global Payments
Segment Reporting Information [Line Items]
Net contribution:	131.2	103.7	89.6
Segment income:	97.4	78.5	68.6
Global Payments | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	172.0	137.3	117.4
Operating revenues:	172.0	137.3	117.4
Net operating revenues (loss):	162.5	129.9	111.5
Total assets:	$ 524.0	$ 243.8	$ 315.9