Segment and Geographic Information - Reportable Segments (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Segment Reporting Information [Line Items]
Total revenues	$ 60,856.1	$ 66,036.0	$ 42,534.2
Operating revenues	2,914.1	2,107.4	1,673.1
Net operating revenues (loss)	1,621.0	1,475.9	1,150.0
Net contribution	1,273.6	1,121.9	868.7
Segment income	763.5	675.7	506.2
Net costs not allocated to operating segments	(463.8)	(398.5)	(355.5)
Gain on acquisitions and other gains, net	23.3	0.0	3.4
Income from operations, before tax	323.0	277.2	154.1
Assets	21,938.7	19,859.6	18,839.6
Corporate Unallocated
Segment Reporting Information [Line Items]
Total revenues	31.7	7.8	1.7
Operating revenues	31.7	7.8	1.7
Net operating revenues (loss)	(62.9)	(59.5)	(54.8)
Assets	812.3	746.3	841.7
Eliminations
Segment Reporting Information [Line Items]
Total revenues	(39.5)	(23.0)	(17.1)
Operating revenues	(39.5)	(23.0)	(17.1)
Commercial
Segment Reporting Information [Line Items]
Net contribution	544.9	415.3	299.7
Segment income	390.7	288.3	192.2
Commercial | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	58,249.2	63,743.2	39,884.0
Operating revenues	862.7	692.1	534.8
Net operating revenues (loss)	721.3	586.5	433.1
Assets	4,676.3	5,931.0	3,969.9
Institutional
Segment Reporting Information [Line Items]
Net contribution	351.5	295.1	260.9
Segment income	217.9	174.6	167.7
Institutional | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	1,513.6	831.8	668.4
Operating revenues	1,513.6	831.8	668.4
Net operating revenues (loss)	532.0	483.5	419.4
Assets	15,059.3	11,687.1	12,403.3
Retail
Segment Reporting Information [Line Items]
Net contribution	212.7	280.3	204.4
Segment income	45.8	115.4	67.8
Retail | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	888.5	1,304.2	1,859.9
Operating revenues	333.0	426.7	348.0
Net operating revenues (loss)	227.3	302.9	222.4
Assets	1,014.2	971.2	1,380.9
Global Payments
Segment Reporting Information [Line Items]
Net contribution	164.5	131.2	103.7
Segment income	109.1	97.4	78.5
Global Payments | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	212.6	172.0	137.3
Operating revenues	212.6	172.0	137.3
Net operating revenues (loss)	203.3	162.5	129.9
Assets	$ 376.6	$ 524.0	$ 243.8