Derivative Financial Instruments - Additional Information (Details) - USD ($) $ in Millions	Mar. 31, 2021	Sep. 30, 2020
Derivative Financial Instruments
Cash collateral derivative counterparty obligations	$ 1.7	$ 3.0

This information is pertaining to the cash collateral posted with certain derivative counterparties against its derivative obligations.

No definition available.

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