Debt - Additional Information (Detail)	1 Months Ended		3 Months Ended		6 Months Ended
	Jun. 30, 2022 USD ($) Days $ / shares shares	Jun. 30, 2019 USD ($) $ / shares shares	Jun. 30, 2022 USD ($) $ / shares	Mar. 31, 2022	Jun. 30, 2022 USD ($) Days $ / shares	Dec. 31, 2021 USD ($)
Debt Instrument [Line Items]
Accumulated deficit	$ (100,394,000)		$ (100,394,000)		$ (100,394,000)	$ (102,087,000)
Additional paid-in capital	687,338,000		687,338,000		687,338,000	724,226,000
Convertible senior notes, net	$ 0		$ 0		$ 0	199,705,000
ASU 2020-06 [Member]
Debt Instrument [Line Items]
Change in Accounting Principle, Accounting Standards Update, Adopted [true false]	true		true		true
Change in Accounting Principle, Accounting Standards Update, Adoption Date	Jan. 01, 2022		Jan. 01, 2022		Jan. 01, 2022
ASU 2020-06 [Member] | Cumulative Effect, Period of Adoption, Adjustment [Member]
Debt Instrument [Line Items]
Accumulated deficit	$ 23,900,000		$ 23,900,000		$ 23,900,000
Additional paid-in capital	50,000,000.0		50,000,000.0		50,000,000.0
Convertible senior notes, net	26,100,000		26,100,000		$ 26,100,000
Convertible Senior Notes Due in 2024 [Member]
Debt Instrument [Line Items]
Debt instrument, aggregate principal amount		$ 230,000,000.0
Debt instrument interest rate		0.25%
Additional principal amount of notes to underwriters		$ 30,000,000.0
Net proceeds from issuance of costs	224,300,000	$ 221,900,000
Debt instrument frequency of periodic payment					semi-annually
Interest payment commencement date		Dec. 01, 2019
Debt instrument maturity date		Jun. 01, 2024
Debt instrument, description					The 2024 Notes bear interest at a rate of 0.25% per year, payable semi-annually in arrears on June 1 and December 1 of each year, commencing December 1, 2019.
Debt instrument, convertible, terms of conversion feature				The 2024 Notes have an initial conversion rate of 21.5049 shares of the Company's Class A common stock per $1,000 principal amount of 2024 Notes, which is equivalent to an initial conversion price of approximately $46.50 per share of its Class A common stock.
Debt instrument repurchased face amount	148,200,000		148,200,000		$ 148,200,000
Repayments of notes payable			192,400,000
Fair value expense recognized			16,600,000		16,600,000
Debt instrument principal outstanding	$ 81,800,000		$ 81,800,000		81,800,000
Debt instrument, convertible, "if-converted value" in excess of the principal amount					$ 10,500,000
Convertible senior notes, net						199,705,000
Convertible Senior Notes Due in 2024 [Member] | ASU 2020-06 [Member]
Debt Instrument [Line Items]
Change in Accounting Principle, Accounting Standards Update, Adoption Date	Jan. 01, 2022		Jan. 01, 2022		Jan. 01, 2022
Convertible Senior Notes Due in 2024 [Member] | ASU 2020-06 [Member] | Cumulative Effect, Period of Adoption, Adjustment [Member]
Debt Instrument [Line Items]
Accumulated deficit	$ 23,900,000		$ 23,900,000		$ 23,900,000
Additional paid-in capital	50,000,000.0		50,000,000.0		50,000,000.0
Convertible senior notes, net	26,100,000		26,100,000		$ 26,100,000
Convertible Senior Notes Due in 2024 [Member] | Class A Common Stock [Member]
Debt Instrument [Line Items]
Debt conversion, converted instrument, shares issued | shares		21.5049
Debt instrument conversion rate principal amount of notes		$ 1,000
Debt instrument convertible initial conversion price per share of common stock | $ / shares		$ 46.50
Convertible Senior Notes Due in 2024 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 1 [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, consecutive trading days | Days					30
Debt Instrument, Redemption Price, Percentage					100.00%
Convertible senior notes due in 2027 [Member]
Debt Instrument [Line Items]
Debt instrument, aggregate principal amount	$ 230,000,000.0		$ 230,000,000.0		$ 230,000,000.0
Debt instrument interest rate	1.75%		1.75%		1.75%
Additional principal amount of notes to initial purchaser's	$ 30,000,000.0		$ 30,000,000.0		$ 30,000,000.0
Debt instrument frequency of periodic payment					semiannually
Interest payment commencement date	Dec. 15, 2022
Debt instrument, description					The 2027 Notes mature on June 15, 2027, unless earlier repurchased, redeemed or converted. The Company may redeem for cash all or, subject to certain limitations, any portion of the 2027 Notes, at its option, on or after June 20, 2025 if the last reported sale price of Altair's Class A Common Stock has been at least 130% of the conversion price then in effect for at least 20 trading days (whether or not consecutive) during any 30 consecutive trading day period, at a redemption price equal to 100% of the principal amount of the notes to be redeemed, plus accrued and unpaid interest to, but excluding, the redemption date. The 2027 Notes bear interest at a rate of 1.750% per year, payable semiannually in arrears on June 15 and December 15 of each year, beginning on December 15, 2022.
Debt instrument conversion rate principal amount of notes	$ 1,000		1,000		$ 1,000
Debt instrument, convertible, terms of conversion feature					The 2027 Notes have an initial conversion rate of 13.9505 shares of the Company's Class A common stock per $1,000 principal amount of 2027 Notes, which is equivalent to an initial conversion price of approximately $71.68 per share of Class A common stock.
Convertible senior notes, net						$ 0
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member]
Debt Instrument [Line Items]
Debt conversion, converted instrument, shares issued | shares	13.9505
Debt instrument conversion rate principal amount of notes	$ 1,000		$ 1,000		$ 1,000
Debt instrument convertible initial conversion price per share of common stock | $ / shares	$ 71.68		$ 71.68		$ 71.68
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 1 [Member]
Debt Instrument [Line Items]
Debt instrument conversion rate principal amount of notes	$ 1,000		$ 1,000		$ 1,000
Debt instrument, convertible, business days | Days	5
Debt instrument, convertible, consecutive trading days | Days	30
Debt instrument, convertible, maximum threshold percentage of sale price of common stock during measurement period	98.00%
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 1 [Member] | Minimum [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, trading days | Days	20				20
Debt instrument, convertible, threshold percentage of conversion price	130.00%				130.00%
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible notes holders conversion rights under circumstances two [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, consecutive trading days | Days	5
Twenty Nineteen Credit Agreement
Debt Instrument [Line Items]
Maturity date					Dec. 15, 2025
Credit facility	$ 150,000,000.0		150,000,000.0		$ 150,000,000.0
Increase in line of credit borrowing capacity	50,000,000.0		50,000,000.0		50,000,000.0
Secured Credit Agreement [Member]
Debt Instrument [Line Items]
Loan outstanding	0		0		0
Amount available for future borrowing	$ 150,000,000.0		$ 150,000,000.0		$ 150,000,000.0