Basic and Diluted Income (Loss) Per Common Share - Basic Income (Loss) Per Common Share to Diluted Income (Loss) Per Common Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Earnings Per Share [Abstract]
Loss from continuing operations	$ (14.2)	$ (29.8)	$ (80.8)	$ (38.7)
Income (loss) attributable to noncontrolling interest and redeemable noncontrolling interest	2.6	2.8	7.0	(9.7)
Loss from continuing operations attributable to the Company	(11.6)	(27.0)	(73.8)	(48.4)
Less: Preferred dividends, deemed dividends and repurchase gains	1.1	0.4	1.7	1.2
Loss from continuing operations attributable to INNOVATE common stockholders	(12.7)	(27.4)	(75.5)	(49.6)
(Loss) income from discontinued operations	(200.3)	8.2	(149.9)	(55.4)
(Loss) income attributable to noncontrolling interest and redeemable noncontrolling interest	0.0	1.5	0.9	16.5
(Loss) income from discontinued operations, net of tax and noncontrolling interest	(200.3)	9.7	(149.0)	(38.9)
Net loss attributable to common stock and participating preferred stockholders	$ (213.0)	$ (17.7)	$ (224.5)	$ (88.5)
Participating shares at end of period:
Weighted-average common stock outstanding (in shares)	77.2	47.4	77.0	46.7
Unvested restricted stock (in shares)	0.0	0.0	0.0	0.0
Preferred stock (as-converted basis) (in shares)	0.0	0.4	0.0	0.1
Total (in shares)	77.2	47.8	77.0	46.8
Percentage of loss allocated to:
Common stock	100.00%	99.20%	100.00%	99.80%
Unvested restricted stock	0.00%	0.00%	0.00%	0.00%
Preferred stock	0.00%	0.80%	0.00%	0.20%
Net loss from continuing operations attributable to common stock, basic	$ (12.7)	$ (27.2)	$ (75.5)	$ (49.5)
Net (loss) income from discontinued operations attributable to common stock, basic	(200.3)	9.6	(149.0)	(38.8)
Net loss attributable to common stock, basic	(213.0)	(17.6)	(224.5)	(88.3)
Earnings allocable to common shares, diluted:
Effect of assumed shares under the if-converted method for convertible instruments	0.0	0.0	0.0	0.0
Net loss from continuing operations attributable to common stock, basic	(12.7)	(27.2)	(75.5)	(49.5)
Net (loss) income from discontinued operations attributable to common stock, basic	(200.3)	9.6	(149.0)	(38.8)
Net loss attributable to common stock, basic	$ (213.0)	$ (17.6)	$ (224.5)	$ (88.3)
Denominator for basic and dilutive earnings per share
Weighted average common shares outstanding - basic (in shares)	77.2	47.4	77.0	46.7
Effect of assumed shares under treasury stock method for stock options and restricted shares and if-converted method for convertible instruments (in shares)	0.0	0.0	0.0	0.0
Weighted average common shares outstanding - diluted (in shares)	77.2	47.4	77.0	46.7
Loss per share - continuing operations
Basic (in usd per share)	$ (0.16)	$ (0.57)	$ (0.98)	$ (1.06)
Diluted (in usd per share)	(0.16)	(0.57)	(0.98)	(1.06)
Loss per common share - discontinued operations
Basic (in usd per share)	(2.59)	0.20	(1.94)	(0.83)
Diluted (in usd per share)	(2.59)	0.20	(1.94)	(0.83)
Loss per share - Net loss attributable to common stock and participating preferred stockholders
Basic (in usd per share)	(2.75)	(0.37)	(2.92)	(1.89)
Diluted (in usd per share)	$ (2.75)	$ (0.37)	$ (2.92)	$ (1.89)