SUPPLEMENTAL DISCLOSURE FOR EARNINGS PER SHARE - (Net income Per Share Information) (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended												12 Months Ended
	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Earnings:
Net income (loss) attributable to First Savings Financial Group, Inc.	$ 15,137	$ 15,405	$ (627)	$ 3,439	$ 5,321	$ 4,392	$ 3,533	$ 2,931	$ 2,744	$ 3,106	$ 1,646	$ 3,406	$ 33,354	$ 16,177	$ 10,902
Shares:
Weighted average common shares outstanding, basic													2,356,680	2,315,697	2,258,020
Net income per common share, basic	$ 6.40	$ 6.51	$ (0.27)	$ 1.47	$ 2.28	$ 1.88	$ 1.53	$ 1.28	$ 1.20	$ 1.37	$ 0.73	$ 1.53	$ 14.15	$ 6.99	$ 4.83
Earnings:
Net income attributable to First Savings Financial Group, Inc.													$ 33,354	$ 16,177	$ 10,902
Shares:
Weighted average common shares outstanding, basic													2,356,680	2,315,697	2,258,020
Add: Dilutive effect of outstanding options													16,180	50,623	107,274
Add: Dilutive effect of restricted stock													3,094	5,764	7,260
Weighted average common shares outstanding, as adjusted													2,375,954	2,372,084	2,372,554
Net income per common share, diluted	$ 6.39	$ 6.51	$ (0.26)	$ 1.44	$ 2.24	$ 1.85	$ 1.50	$ 1.24	$ 1.15	$ 1.31	$ 0.69	$ 1.44	$ 14.04	$ 6.82	$ 4.60