Subsequent Events (Details) - USD ($) $ / shares in Units, $ in Millions		3 Months Ended
	Apr. 17, 2026	Mar. 31, 2026	Mar. 31, 2025
Madison Industries IAQ Solutions Corporation
Subsequent Event [Line Items]
Cash paid for interest		$ 66.1	$ 45.9
Subsequent Event
Subsequent Event [Line Items]
Proceeds from issuance of common stock	$ 2,584.2
Subsequent Event | Common Stock
Subsequent Event [Line Items]
Stock canceled during period (in shares)	1,000
Subsequent Event | Credit Agreement | Line of Credit
Subsequent Event [Line Items]
Cash	$ 77.1
Repayments of notes payable	2,661.2
Subsequent Event | Incremental Term Loan | Line of Credit | Senior secured notes
Subsequent Event [Line Items]
Debt repaid, principal	158.4
Cash paid for interest	41.6
Subsequent Event | Initial Term Loan | Line of Credit | Senior secured notes
Subsequent Event [Line Items]
Debt repaid, principal	2,425.7
Cash paid for interest	$ 35.5
Subsequent Event | Common Class A
Subsequent Event [Line Items]
EAR unit conversion per share (in shares)	1
Subsequent Event | IPO | Common Class A
Subsequent Event [Line Items]
Sale of stock (in shares)	95,096,154
Sale of stock (in dollars per share)	$ 27.00
Subsequent Event | Private Placement | Common Class B
Subsequent Event [Line Items]
Sale of stock (in shares)	3,703,704
Sale of stock (in dollars per share)	$ 27.00
Subsequent Event | Madison Industries IAQ Solutions Corporation | Common Stock
Subsequent Event [Line Items]
Stock canceled during period (in shares)	1,000
Subsequent Event | Madison Industries IAQ Solutions Corporation | Credit Agreement | Line of Credit
Subsequent Event [Line Items]
Cash	$ 77.1
Repayments of notes payable	2,661.2
Debt repaid, principal	2,584.2
Subsequent Event | Madison Industries IAQ Solutions Corporation | Incremental Term Loan | Line of Credit | Senior secured notes
Subsequent Event [Line Items]
Cash paid for interest	41.6
Subsequent Event | Madison Industries IAQ Solutions Corporation | Initial Term Loan | Line of Credit | Senior secured notes
Subsequent Event [Line Items]
Cash paid for interest	$ 35.5
Subsequent Event | Madison Industries IAQ Solutions Corporation | Common Class A
Subsequent Event [Line Items]
EAR unit conversion per share (in shares)	1
Subsequent Event | Madison Industries US
Subsequent Event [Line Items]
Percent of outstanding equity interests distributed	100.00%
Subsequent Event | Holdings | Madison Industries IAQ Solutions Corporation
Subsequent Event [Line Items]
Ownership percentage	100.00%
Subsequent Event | Holdings | Madison Air Solutions Corporation
Subsequent Event [Line Items]
Ownership percentage	100.00%
Subsequent Event | Madison Air Solutions Corporation | Madison Industries IAQ Solutions Corporation
Subsequent Event [Line Items]
Ownership percentage	100.00%