Earnings Per Share - Computation (Details) - Madison Industries IAQ Solutions Corporation - USD ($) $ / shares in Units, $ in Millions	3 Months Ended
	Mar. 31, 2026	Mar. 31, 2025
Earnings Per Share [Line Items]
Income (loss) from continuing operations	$ 33.6	$ 36.8
Weighted-average shares outstanding - basic (in shares)	1,000	1,000
Effect of dilutive securities (in shares)	0	0
Weighted-average shares outstanding - diluted (in shares)	1,000	1,000
Earnings per share:
Net earnings per share - basic (in dollars per share)	$ 33,617	$ 36,762
Net earnings per share - diluted (in dollars per share)	$ 33,617	$ 36,762