Loans and Allowance for Loan Losses - Recorded Investment in Troubled Debt Restructurings by Class of Loan and Accrual Status (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Sep. 30, 2020
Financing Receivable, Modifications [Line Items]
Accruing	$ 2,019	$ 3,069
Nonaccrual	5,978	6,794
Total	7,997	9,863
Residential real estate [Member]
Financing Receivable, Modifications [Line Items]
Accruing	1,407	2,562
Nonaccrual		116
Total	1,407	2,678
Commercial real estate [Member]
Financing Receivable, Modifications [Line Items]
Accruing	438	449
Nonaccrual	489	512
Total	927	961
SBA commercial real estate
Financing Receivable, Modifications [Line Items]
Nonaccrual	3,296	3,800
Total	3,296	3,800
Multifamily
Financing Receivable, Modifications [Line Items]
Nonaccrual	648	698
Total	648	698
Commercial Business
Financing Receivable, Modifications [Line Items]
Accruing	124	2
Nonaccrual	1,545	1,668
Total	1,669	1,670
Consumer
Financing Receivable, Modifications [Line Items]
Accruing	50	56
Total	$ 50	$ 56

Financing Receivable, Modifications, Recorded Investment, Accruing

No definition available.

Name:	fsfg_FinancingReceivableModificationsRecordedInvestmentAccruing
Namespace Prefix:	fsfg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Financing Receivable, Modifications, Recorded Investment, Nonaccrual

+ References

No definition available.

+ Details

Name:	fsfg_FinancingReceivableModificationsRecordedInvestmentNonaccrual
Namespace Prefix:	fsfg_
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_FinancingReceivableModificationsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of financing receivable modified as troubled debt restructuring.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 33
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953676-111524

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 40
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=121585226&loc=d3e18845-111554

+ Details

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

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ResidentialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fsfg_SbaCommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=srt_MultifamilyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConsumerLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: