Fair Value Measurements - Summary of Gross Unrealized Gains and Losses of Marketable Securities (Detail) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	$ 1,397,442	$ 438,052
Gross Unrealized Gains	161	451
Gross Unrealized Losses	(446)	(36)
Fair Value	1,397,157	438,467
U.S. Government Securities [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	247,289	160,589
Gross Unrealized Gains	6	11
Gross Unrealized Losses	(78)	(12)
Fair Value	247,217	160,588
U.S. Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	521,373	122,882
Gross Unrealized Gains	99	240
Gross Unrealized Losses	(229)	(15)
Fair Value	521,243	123,107
International Corporate Bonds [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	259,127	57,485
Gross Unrealized Gains	51	200
Gross Unrealized Losses	(130)	(9)
Fair Value	259,048	57,676
U.S. Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	153,337	45,963
Gross Unrealized Gains	2
Gross Unrealized Losses	(4)
Fair Value	153,335	45,963
International Commercial Paper [Member]
Schedule of Available-for-sale Securities [Line Items]
Amortized Cost	216,316	51,133
Gross Unrealized Gains	3
Gross Unrealized Losses	(5)
Fair Value	$ 216,314	$ 51,133

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 http://asc.fasb.org/extlink&oid=121645371&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 http://asc.fasb.org/extlink&oid=121645371&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 http://asc.fasb.org/extlink&oid=121645371&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 http://asc.fasb.org/extlink&oid=121558606&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 http://asc.fasb.org/extlink&oid=121558606&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 http://asc.fasb.org/extlink&oid=121553693&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: