Debt - Additional Information (Detail)	1 Months Ended			12 Months Ended
	Dec. 31, 2022 USD ($) Days $ / shares	Jun. 30, 2022 USD ($)	Jun. 30, 2019 USD ($) $ / shares shares	Dec. 31, 2022 USD ($) Days $ / shares shares	Nov. 07, 2022 USD ($)	Dec. 31, 2021 USD ($)
Debt Instrument [Line Items]
Accumulated deficit	$ (121,577,000)			$ (121,577,000)		$ (102,087,000)
Additional paid-in capital	721,307,000			721,307,000		724,226,000
Convertible senior notes, net	$ 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
Change in Accounting Principle, Accounting Standards Update, Adoption Date	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
Additional paid-in capital	50,000,000.0			50,000,000.0
Convertible senior notes, net	26,100,000			26,100,000
Overdraft and Line of Credit [Member]
Debt Instrument [Line Items]
Loan outstanding	0			0		0
Amount available under secured credit agreement	$ 3,100,000			$ 3,100,000		3,300,000
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%		0.25%	0.25%
Additional principal amount of notes to underwriters			$ 30,000,000.0
Net proceeds from issuance of costs			$ 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 interest rate is fixed at 0.25% per year, payable semi-annually in arrears on June 1 and December 1 of each year, which commenced on December 1, 2019.
Debt instrument conversion rate principal amount of notes	$ 1,000			$ 1,000
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
Repayments of notes payable				192,400,000
Fair value expense recognized				16,600,000
Debt instrument principal outstanding	$ 81,800,000			$ 81,800,000
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
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
Additional paid-in capital	50,000,000.0			50,000,000.0
Convertible senior notes, net	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 conversion rate principal amount of notes	$ 1,000			$ 1,000
Debt instrument, convertible, business days | Days	5
Debt instrument, convertible, consecutive trading days | Days	30			30
Debt instrument, convertible, maximum threshold percentage of sale price of common stock during measurement period	98.00%
Debt Instrument, Redemption Price, Percentage				100.00%
Convertible Senior Notes Due in 2024 [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
Debt instrument, convertible, threshold percentage of conversion price	130.00%
Convertible Senior Notes Due in 2024 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 2 [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, consecutive trading days | Days	5
Convertible senior notes due in 2027 [Member]
Debt Instrument [Line Items]
Debt instrument, aggregate principal amount		$ 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
Net proceeds from issuance of costs		$ 224,300,000
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, which commenced on December 15, 2022.
Debt instrument conversion rate principal amount of notes	$ 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
Increase in line of credit borrowing capacity					$ 50,000,000.0
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
Debt instrument convertible initial conversion price per share of common stock | $ / shares	$ 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
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, Circumstances 2 [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, consecutive trading days | Days	5
Twenty Nineteen Credit Agreement
Debt Instrument [Line Items]
Maturity date				Dec. 31, 2025
Credit facility	$ 200,000,000.0			$ 200,000,000.0
Increase in unrestricted domestic cash				$ 20,000,000.0
Twenty Nineteen Credit Agreement | Federal Funds Effective Swap Rate [Member]
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				0.50%
Twenty Nineteen Credit Agreement | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				1.00%
Twenty Nineteen Credit Agreement | Minimum [Member]
Debt Instrument [Line Items]
Commitment fees on unused portion of the Revolving Credit Facility				0.15%
Twenty Nineteen Credit Agreement | Minimum [Member] | Term Benchmark Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1.25%			1.25%
Twenty Nineteen Credit Agreement | Minimum [Member] | Swingline Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	0.25%			0.25%
Twenty Nineteen Credit Agreement | Minimum [Member] | ABR Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	0.25%			0.25%
Twenty Nineteen Credit Agreement | Maximum [Member]
Debt Instrument [Line Items]
Commitment fees on unused portion of the Revolving Credit Facility				0.30%
Senior secured leverage ratio				3.00%
Twenty Nineteen Credit Agreement | Maximum [Member] | Term Benchmark Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	2.00%			2.00%
Twenty Nineteen Credit Agreement | Maximum [Member] | Swingline Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1.00%			1.00%
Twenty Nineteen Credit Agreement | Maximum [Member] | ABR Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1.00%			1.00%
Secured Credit Agreement [Member]
Debt Instrument [Line Items]
Loan outstanding	$ 0			$ 0