Fair Value Measurements - Summary of Gross Unrealized Gains and Losses of Marketable Securities (Detail) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	$ 1,321,069	$ 1,450,723
Gross Unrealized Gains	22	27
Gross Unrealized Losses	(13,894)	(2,687)
Fair Value	1,307,197	1,448,063
U.S. Government Securities [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	408,463	325,514
Gross Unrealized Gains	19
Gross Unrealized Losses	(5,843)	(982)
Fair Value	402,639	324,532
U.S. Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	498,829	628,836
Gross Unrealized Gains	3	27
Gross Unrealized Losses	(4,815)	(1,083)
Fair Value	494,017	627,780
International Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	167,534	237,303
Gross Unrealized Losses	(2,138)	(491)
Fair Value	165,396	236,812
U.S. Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	74,170	80,194
Gross Unrealized Losses	(133)	(18)
Fair Value	74,037	80,176
International Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	114,107	142,358
Gross Unrealized Losses	(253)	(23)
Fair Value	113,854	142,335
U.S. Certificates of Deposit [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	19,981
Fair Value	19,981
U.S. Municipal Securities [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	37,985	36,518
Gross Unrealized Losses	(712)	(90)
Fair Value	$ 37,273	$ 36,428

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

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

- Definition

Amortized cost of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis
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), classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=124260329&loc=d3e26626-111562

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent
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_CertificatesOfDepositMember
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: