Area of office space in square feet.

No definition available.

Name:	sage_AreaOfOfficeSpace
Namespace Prefix:	sage_
Data Type:	num:areaItemType
Balance Type:	na
Period Type:	duration

- Definition

Commitments and contingencies.

+ References

No definition available.

+ Details

Name:	sage_CommitmentsAndContingenciesLineItems
Namespace Prefix:	sage_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Increase in area of office space.

+ References

No definition available.

+ Details

Name:	sage_IncreaseInAreaOfOfficeSpace
Namespace Prefix:	sage_
Data Type:	num:areaItemType
Balance Type:	na
Period Type:	duration

- Definition

Lessor operating lease remaining lease rerms.

+ References

No definition available.

+ Details

Name:	sage_LessorOperatingLeaseRemainingLeaseTerms
Namespace Prefix:	sage_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Date which lease or group of leases is set to expire, in CCYY-MM-DD format.

+ References

No definition available.

+ Details

Name:	us-gaap_LeaseExpirationDate1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of terms and conditions of option to extend lessor's operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 30
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-URI http://asc.fasb.org/extlink&oid=119202524&loc=SL77919359-209981

+ Details

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

- Definition

Term of lessor's operating lease renewal, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 30
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-URI http://asc.fasb.org/extlink&oid=119202524&loc=SL77919359-209981

+ Details

Name:	us-gaap_LessorOperatingLeaseRenewalTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_LeaseArrangementTypeAxis=sage_OperatingLeaseOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LeaseArrangementTypeAxis=sage_OperatingLeaseTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LeaseArrangementTypeAxis=sage_OperatingLeaseThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LeaseArrangementTypeAxis=sage_OperatingLeaseFiveMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Leases, Commitments and Contingencies - Operating Leases - Additional Information (Detail) - ft²			1 Months Ended			3 Months Ended
	Feb. 28, 2019	Jan. 01, 2019	Mar. 31, 2019	Dec. 31, 2018	May 31, 2018	Mar. 31, 2020
Commitments And Contingencies [Line Items]
Operating lease option to extend						true
Operating lease renewal term						5 years
Operating Lease One [Member]
Commitments And Contingencies [Line Items]
Office space rent under operating lease	58,442	58,442	63,017
Lease expire date		Aug. 15, 2024	Aug. 31, 2024
Increased office space rent			4,575
Operating Lease Two [Member]
Commitments And Contingencies [Line Items]
Office space rent under operating lease		40,419
Lease expire date		Aug. 31, 2024
Operating Lease Three [Member]
Commitments And Contingencies [Line Items]
Office space rent under operating lease					15,525
Lease expire date					Nov. 30, 2024
Operating Lease Five [Member]
Commitments And Contingencies [Line Items]
Office space rent under operating lease				15,975
Lease expire date				Feb. 29, 2024
Minimum [Member]
Commitments And Contingencies [Line Items]
Operating lease remaining lease terms						1 year
Maximum [Member]
Commitments And Contingencies [Line Items]
Operating lease remaining lease terms						6 years