Subsequent Events (Details) - Subsequent Event $ / shares in Units, $ in Millions	Apr. 17, 2026 USD ($) $ / shares shares
Subsequent Event [Line Items]
Proceeds from issuance of common stock	$ 2,584.2
Common stock, outstanding, percent	1.50%
Common Stock
Subsequent Event [Line Items]
Stock canceled during period (in shares) | shares	1,000
Madison Industries US
Subsequent Event [Line Items]
Percent of outstanding equity interests distributed	100.00%
Holdings | Madison Industries IAQ Solutions Corporation
Subsequent Event [Line Items]
Ownership percentage	100.00%
Holdings | Madison Air Solutions Corporation
Subsequent Event [Line Items]
Ownership percentage	100.00%
Credit Agreement | Line of Credit
Subsequent Event [Line Items]
Cash	$ 77.1
Repayments of notes payable	2,661.2
Incremental Term Loan | Line of Credit | Senior secured notes
Subsequent Event [Line Items]
Debt repaid, principal	158.4
Cash paid for interest	41.6
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
Common Class A
Subsequent Event [Line Items]
EAR unit conversion per share (in shares) | shares	1
Common stock reserved for future issuance (in shares) | shares	44,003,369
IPO | Common Class A
Subsequent Event [Line Items]
Sale of stock (in shares) | shares	95,096,154
Sale of stock (in dollars per share) | $ / shares	$ 27.00
Private Placement | Common Class B
Subsequent Event [Line Items]
Sale of stock (in shares) | shares	3,703,704
Sale of stock (in dollars per share) | $ / shares	$ 27.00