Goodwill and Other Intangible Assets - Other Intangibles (Details) - USD ($)	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Other intangible assets
Amortized intangible assets, carrying amount	$ 795,900,000	$ 453,500,000
Amortized intangible assets, accumulated amortization	360,300,000	303,100,000
Amortized intangible assets, net	435,600,000	150,400,000
Total other intangible assets, carrying amount	839,600,000	497,200,000
Total other intangible assets, net	479,300,000	194,100,000
Intangible asset amortization expense	50,200,000	26,000,000.0	$ 28,200,000
Goodwill and Other Intangible Assets (Textuals) [Abstract]
Estimated amortization expense in 2020	53,900,000
Estimated amortization expense in 2021	51,000,000.0
Estimated amortization expense in 2022	49,700,000
Estimated amortization expense in 2023	46,800,000
Estimated amortization expense in 2024	44,600,000
Goodwill and intangible asset impairment	0
Computer software products
Other intangible assets
Amortized intangible assets, carrying amount	192,700,000	190,600,000
Amortized intangible assets, accumulated amortization	139,000,000.0	128,300,000
Amortized intangible assets, net	53,700,000	62,300,000
Intangible asset amortization expense	10,200,000	10,400,000	$ 11,800,000
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	351,300,000	110,500,000
Amortized intangible assets, accumulated amortization	92,500,000	69,200,000
Amortized intangible assets, net	258,800,000	41,300,000
Technology
Other intangible assets
Amortized intangible assets, carrying amount	165,800,000	110,400,000
Amortized intangible assets, accumulated amortization	84,000,000.0	69,500,000
Amortized intangible assets, net	81,800,000	40,900,000
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	71,700,000	31,400,000
Amortized intangible assets, accumulated amortization	31,300,000	26,400,000
Amortized intangible assets, net	40,400,000	5,000,000.0
Other
Other intangible assets
Amortized intangible assets, carrying amount	14,400,000	10,600,000
Amortized intangible assets, accumulated amortization	13,500,000	9,700,000
Amortized intangible assets, net	900,000	900,000
Trademarks
Other intangible assets
Allen-Bradley® trademark not subject to amortization	$ (43,700,000)	$ (43,700,000)