Fair Value Measurements - Summary of Fair Value And Unrealized Losses of Marketable Securities In Loss Position (Detail) - USD ($) $ in Thousands	Mar. 31, 2023	Dec. 31, 2022
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	$ 430,420	$ 513,738
Less than 12 months, Unrealized Losses	(2,322)	(4,795)
Greater than 12 months, Fair Value	253,971	399,783
Greater than 12 months, Unrealized Losses	(3,251)	(5,455)
Fair Value	684,391	913,521
Unrealized Losses	(5,573)	(10,250)
U.S. Government Securities [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	59,680	112,243
Less than 12 months, Unrealized Losses	(548)	(1,517)
Greater than 12 months, Fair Value	108,845	185,691
Greater than 12 months, Unrealized Losses	(1,601)	(2,745)
Fair Value	168,525	297,934
Unrealized Losses	(2,149)	(4,262)
U.S. Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	144,665	208,507
Less than 12 months, Unrealized Losses	(978)	(1,989)
Greater than 12 months, Fair Value	88,097	130,633
Greater than 12 months, Unrealized Losses	(830)	(1,541)
Fair Value	232,762	339,140
Unrealized Losses	(1,808)	(3,530)
International Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	36,432	50,982
Less than 12 months, Unrealized Losses	(213)	(497)
Greater than 12 months, Fair Value	35,015	68,993
Greater than 12 months, Unrealized Losses	(341)	(636)
Fair Value	71,447	119,975
Unrealized Losses	(554)	(1,133)
U.S. Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	36,712	24,768
Less than 12 months, Unrealized Losses	(103)	(120)
Fair Value	36,712	24,768
Unrealized Losses	(103)	(120)
International Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	95,624	30,987
Less than 12 months, Unrealized Losses	(181)	(175)
Fair Value	95,624	30,987
Unrealized Losses	(181)	(175)
U.S. Municipal Securities [Member]
Schedule of Available-for-sale Securities [Line Items]
Less than 12 months, Fair Value	57,307	86,251
Less than 12 months, Unrealized Losses	(299)	(497)
Greater than 12 months, Fair Value	22,014	14,466
Greater than 12 months, Unrealized Losses	(479)	(533)
Fair Value	79,321	100,717
Unrealized Losses	$ (778)	$ (1,030)

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in continuous unrealized loss position for more than 12 months, without allowance for credit loss. Includes beneficial interest in securitized financial asset.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 50
-Paragraph 5
-URI https://asc.fasb.org/extlink&oid=124269663&loc=SL82922890-210455

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 7
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27337-111563

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 55
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=121590138&loc=SL82922954-210456

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of accumulated unrealized loss on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in continuous unrealized loss position for 12 months or longer, without allowance for credit loss. Includes beneficial interest in securitized financial asset.

+ References

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in continuous unrealized loss position for less than 12 months, without allowance for credit loss. Includes beneficial interest in securitized financial asset.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 7
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27337-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 50
-Paragraph 5
-URI https://asc.fasb.org/extlink&oid=124269663&loc=SL82922890-210455

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 55
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=121590138&loc=SL82922954-210456

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of accumulated unrealized loss on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in continuous unrealized loss position for less than 12 months, without allowance for credit loss. Includes beneficial interest in securitized financial asset.

+ References

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in unrealized loss position without allowance for credit loss.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 6
-Subparagraph (a)(1)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27290-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 50
-Paragraph 4
-Subparagraph (a)(1)
-URI https://asc.fasb.org/extlink&oid=124269663&loc=SL82922888-210455

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 55
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=121590138&loc=SL82922954-210456

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of accumulated unrealized loss on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), in unrealized loss position, without allowance for credit loss. Includes beneficial interest in securitized financial asset.

+ References

+ Details

Name:	us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_USTreasurySecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_CorporateBondSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=sage_InternationalCorporateBondsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_CommercialPaperMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=sage_InternationalCommercialPaperMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InvestmentTypeAxis=us-gaap_MunicipalBondsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: