Condensed Consolidated Statements of Shareholder's Equity - SB/RH - USD ($) $ in Millions	Total	Total Shareholders' Equity	Accumulated Earnings	Accumulated Other Comprehensive Loss	Non- controlling Interest	SB/RH	SB/RH Total Shareholders' Equity	SB/RH Other Capital	SB/RH Accumulated Earnings	SB/RH Accumulated Other Comprehensive Loss	SB/RH Non- controlling Interest
Balances at beginning of period at Sep. 30, 2022	$ 1,269.1	$ 1,263.2	$ 362.1	$ (303.1)	$ 5.9	$ 1,133.1	$ 1,125.6	$ 2,164.6	$ (736.0)	$ (303.0)	$ 7.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	(40.0)	(40.3)	(40.3)		0.3	(39.8)	(40.1)		(40.1)		0.3
Income from discontinued operations, net of tax	19.5	19.4	19.4		0.1	19.5	19.4		19.4		0.1
Other comprehensive income, net of tax	14.5	14.2		14.2	0.3	14.5	14.2			14.2	0.3
Restricted stock issued and related tax withholdings	(10.5)	(10.5)				(10.5)	(10.5)	(10.5)
Share based compensation	4.1	4.1				3.9	3.9	3.9
Dividends paid to parent						(17.1)	(17.1)		(17.1)
Balances at end of period at Jan. 01, 2023	1,239.4	1,232.8	323.9	(288.9)	6.6	1,103.6	1,095.4	2,158.0	(773.8)	(288.8)	8.2
Balances at beginning of period at Sep. 30, 2022	1,269.1	1,263.2	362.1	(303.1)	5.9	1,133.1	1,125.6	2,164.6	(736.0)	(303.0)	7.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	(115.0)					(115.0)
Income from discontinued operations, net of tax	40.9					41.4
Other comprehensive income, net of tax	30.7					30.7
Balances at end of period at Apr. 02, 2023	1,189.1	1,182.2	252.6	(272.9)	6.9	1,053.7	1,045.2	2,162.4	(844.4)	(272.8)	8.5
Balances at beginning of period at Jan. 01, 2023	1,239.4	1,232.8	323.9	(288.9)	6.6	1,103.6	1,095.4	2,158.0	(773.8)	(288.8)	8.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	(75.0)	(75.1)	(75.1)		0.1	(75.2)	(75.3)		(75.3)		0.1
Income from discontinued operations, net of tax	21.4	21.4	21.4			21.9	21.9		21.9
Other comprehensive income, net of tax	16.2	16.0		16.0	0.2	16.2	16.0			16.0	0.2
Share based compensation	4.7	4.7				4.4	4.4	4.4
Dividends paid to parent						(17.2)	(17.2)		(17.2)
Balances at end of period at Apr. 02, 2023	1,189.1	1,182.2	252.6	(272.9)	6.9	1,053.7	1,045.2	2,162.4	(844.4)	(272.8)	8.5
Balances at beginning of period at Sep. 30, 2023	2,518.3	2,517.6	2,096.0	(249.4)	0.7	2,689.7	2,687.4	2,168.9	767.8	(249.3)	2.3
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	17.5	17.4	17.4		0.1	18.2	18.1		18.1		0.1
Income from discontinued operations, net of tax	11.7	11.7	11.7			11.7	11.7		11.7
Other comprehensive income, net of tax	16.3	16.2		16.2	0.1	16.3	16.2			16.2	0.1
Restricted stock issued and related tax withholdings	(5.4)	(5.4)				(5.4)	(5.4)	(5.4)
Share based compensation	3.9	3.9				3.8	3.8	3.8
Dividends paid to parent						(246.1)	(246.1)		(246.1)
Balances at end of period at Dec. 31, 2023	2,301.7	2,300.8	2,110.6	(233.2)	0.9	2,488.2	2,485.7	2,167.3	551.5	(233.1)	2.5
Balances at beginning of period at Sep. 30, 2023	2,518.3	2,517.6	2,096.0	(249.4)	0.7	2,689.7	2,687.4	2,168.9	767.8	(249.3)	2.3
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	67.4					68.5
Income from discontinued operations, net of tax	22.7					22.7
Other comprehensive income, net of tax	18.2					18.2
Balances at end of period at Mar. 31, 2024	2,257.5	2,256.9	2,158.8	(231.2)	0.6	2,445.4	2,443.2	2,171.4	502.9	(231.1)	2.2
Balances at beginning of period at Dec. 31, 2023	2,301.7	2,300.8	2,110.6	(233.2)	0.9	2,488.2	2,485.7	2,167.3	551.5	(233.1)	2.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income from continuing operations	49.9	50.1	50.1		(0.2)	50.4	50.6		50.6		(0.2)
Income from discontinued operations, net of tax	11.0	11.0	11.0		0.0	11.0	11.0		11.0
Other comprehensive income, net of tax	1.9	2.0		2.0	(0.1)	1.9	2.0			2.0	(0.1)
Share based compensation	4.5	4.5				4.1	4.1	4.1
Dividends paid to parent						(110.2)	(110.2)		(110.2)
Balances at end of period at Mar. 31, 2024	$ 2,257.5	$ 2,256.9	$ 2,158.8	$ (231.2)	$ 0.6	$ 2,445.4	$ 2,443.2	$ 2,171.4	$ 502.9	$ (231.1)	$ 2.2