F Distribution Table

The F distribution table gives critical F values for ANOVA and variance-ratio tests — entered with two degrees of freedom, numerator across the top and denominator down the side, at α = 0.05 and α = 0.01.

F critical values at α = 0.05

F critical values at alpha = 0.05: columns = numerator df, rows = denominator df
df2 \ df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120
1	161.45	199.50	215.71	224.58	230.16	233.99	236.77	238.88	240.54	241.88	243.91	245.95	248.01	249.05	250.10	251.14	252.20	253.25
2	18.51	19.00	19.16	19.25	19.30	19.33	19.35	19.37	19.38	19.40	19.41	19.43	19.45	19.45	19.46	19.47	19.48	19.49
3	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.81	8.79	8.74	8.70	8.66	8.64	8.62	8.59	8.57	8.55
4	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	6.00	5.96	5.91	5.86	5.80	5.77	5.75	5.72	5.69	5.66
5	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.77	4.74	4.68	4.62	4.56	4.53	4.50	4.46	4.43	4.40
6	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.10	4.06	4.00	3.94	3.87	3.84	3.81	3.77	3.74	3.70
7	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.68	3.64	3.57	3.51	3.44	3.41	3.38	3.34	3.30	3.27
8	5.32	4.46	4.07	3.84	3.69	3.58	3.50	3.44	3.39	3.35	3.28	3.22	3.15	3.12	3.08	3.04	3.01	2.97
9	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.18	3.14	3.07	3.01	2.94	2.90	2.86	2.83	2.79	2.75
10	4.96	4.10	3.71	3.48	3.33	3.22	3.14	3.07	3.02	2.98	2.91	2.85	2.77	2.74	2.70	2.66	2.62	2.58
12	4.75	3.89	3.49	3.26	3.11	3.00	2.91	2.85	2.80	2.75	2.69	2.62	2.54	2.51	2.47	2.43	2.38	2.34
15	4.54	3.68	3.29	3.06	2.90	2.79	2.71	2.64	2.59	2.54	2.48	2.40	2.33	2.29	2.25	2.20	2.16	2.11
20	4.35	3.49	3.10	2.87	2.71	2.60	2.51	2.45	2.39	2.35	2.28	2.20	2.12	2.08	2.04	1.99	1.95	1.90
24	4.26	3.40	3.01	2.78	2.62	2.51	2.42	2.36	2.30	2.25	2.18	2.11	2.03	1.98	1.94	1.89	1.84	1.79
30	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.21	2.16	2.09	2.01	1.93	1.89	1.84	1.79	1.74	1.68
40	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.12	2.08	2.00	1.92	1.84	1.79	1.74	1.69	1.64	1.58
60	4.00	3.15	2.76	2.53	2.37	2.25	2.17	2.10	2.04	1.99	1.92	1.84	1.75	1.70	1.65	1.59	1.53	1.47
120	3.92	3.07	2.68	2.45	2.29	2.18	2.09	2.02	1.96	1.91	1.83	1.75	1.66	1.61	1.55	1.50	1.43	1.35
∞	3.84	3.00	2.60	2.37	2.21	2.10	2.01	1.94	1.88	1.83	1.75	1.67	1.57	1.52	1.46	1.39	1.32	1.22

F critical values at α = 0.01

F critical values at alpha = 0.01: columns = numerator df, rows = denominator df
df2 \ df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120
1	4052.18	4999.50	5403.35	5624.58	5763.65	5858.99	5928.36	5981.07	6022.47	6055.85	6106.32	6157.28	6208.73	6234.63	6260.65	6286.78	6313.03	6339.39
2	98.50	99.00	99.17	99.25	99.30	99.33	99.36	99.37	99.39	99.40	99.42	99.43	99.45	99.46	99.47	99.47	99.48	99.49
3	34.12	30.82	29.46	28.71	28.24	27.91	27.67	27.49	27.35	27.23	27.05	26.87	26.69	26.60	26.50	26.41	26.32	26.22
4	21.20	18.00	16.69	15.98	15.52	15.21	14.98	14.80	14.66	14.55	14.37	14.20	14.02	13.93	13.84	13.75	13.65	13.56
5	16.26	13.27	12.06	11.39	10.97	10.67	10.46	10.29	10.16	10.05	9.89	9.72	9.55	9.47	9.38	9.29	9.20	9.11
6	13.75	10.92	9.78	9.15	8.75	8.47	8.26	8.10	7.98	7.87	7.72	7.56	7.40	7.31	7.23	7.14	7.06	6.97
7	12.25	9.55	8.45	7.85	7.46	7.19	6.99	6.84	6.72	6.62	6.47	6.31	6.16	6.07	5.99	5.91	5.82	5.74
8	11.26	8.65	7.59	7.01	6.63	6.37	6.18	6.03	5.91	5.81	5.67	5.52	5.36	5.28	5.20	5.12	5.03	4.95
9	10.56	8.02	6.99	6.42	6.06	5.80	5.61	5.47	5.35	5.26	5.11	4.96	4.81	4.73	4.65	4.57	4.48	4.40
10	10.04	7.56	6.55	5.99	5.64	5.39	5.20	5.06	4.94	4.85	4.71	4.56	4.41	4.33	4.25	4.17	4.08	4.00
12	9.33	6.93	5.95	5.41	5.06	4.82	4.64	4.50	4.39	4.30	4.16	4.01	3.86	3.78	3.70	3.62	3.54	3.45
15	8.68	6.36	5.42	4.89	4.56	4.32	4.14	4.00	3.89	3.80	3.67	3.52	3.37	3.29	3.21	3.13	3.05	2.96
20	8.10	5.85	4.94	4.43	4.10	3.87	3.70	3.56	3.46	3.37	3.23	3.09	2.94	2.86	2.78	2.69	2.61	2.52
24	7.82	5.61	4.72	4.22	3.90	3.67	3.50	3.36	3.26	3.17	3.03	2.89	2.74	2.66	2.58	2.49	2.40	2.31
30	7.56	5.39	4.51	4.02	3.70	3.47	3.30	3.17	3.07	2.98	2.84	2.70	2.55	2.47	2.39	2.30	2.21	2.11
40	7.31	5.18	4.31	3.83	3.51	3.29	3.12	2.99	2.89	2.80	2.66	2.52	2.37	2.29	2.20	2.11	2.02	1.92
60	7.08	4.98	4.13	3.65	3.34	3.12	2.95	2.82	2.72	2.63	2.50	2.35	2.20	2.12	2.03	1.94	1.84	1.73
120	6.85	4.79	3.95	3.48	3.17	2.96	2.79	2.66	2.56	2.47	2.34	2.19	2.03	1.95	1.86	1.76	1.66	1.53
∞	6.63	4.61	3.78	3.32	3.02	2.80	2.64	2.51	2.41	2.32	2.18	2.04	1.88	1.79	1.70	1.59	1.47	1.32

How to read the F table

An F statistic is a ratio of two variance estimates, so it carries two degrees of freedom: the numerator's (df1, columns) and the denominator's (df2, rows). In one-way ANOVA with k groups and N total observations, df1 = k − 1 and df2 = N − k. Worked example: three groups, 33 observations — df1 = 2, df2 = 30. At α = 0.05, run down the rows to 30 and across the columns to 2: the critical value is 3.32 (check the table: row 30, column 2). A computed F of 4.6 exceeds it, significant at 0.05; against the α = 0.01 table (5.39), it does not reach 0.01 significance. The other anchor cell worth knowing: F(2, 10) at 0.05 is 4.10 — small samples demand big ratios, which is the table's whole personality: with little data, only dramatic variance differences convince.

What F tests are deciding

ANOVA asks whether group means differ more than within-group noise can explain: F = (variance between groups) / (variance within groups). An F near 1 says the groups differ by about what chance predicts; large F says the between-group signal swamps the noise. The same table serves the direct variance-ratio test (is one population more variable than another?) used in quality engineering. Two cautions travel with the table: F tests are sensitive to non-normality — heavy-tailed data inflates F — and an omnibus-significant ANOVA says only that some group differs, not which; follow-ups (with their own error control) do that work. The family connections are elegant: square a t statistic and you get an F with df1 = 1, and the statistics tables hub explains how all five tables on this site descend from the normal distribution.

Reading an ANOVA result against the table

Software prints ANOVA tables with an F and a p-value, but the printed-table skill is what lets you audit one at a glance. A study with 4 groups and 25 observations reports F = 3.90: df1 = 3, df2 = 21. In the α = 0.05 table, the critical value near that cell (df2 = 20, df1 = 3) is 3.10, and at df2 = 24 it is 3.01 — so 3.90 clears the 0.05 line with room, and in the α = 0.01 table (4.94 at (3, 20)) it does not reach 0.01. The honest one-line summary is "significant at 0.05, not at 0.01" — the same bracketing discipline as every other table on this site. A second anchor for calibration: F(4, 24) at 0.05 is 2.78, so a reported F of 2.4 with those degrees of freedom is not significant however the surrounding prose leans.

Values computed from the F distribution's cumulative function · Verified November 2026

Frequently asked questions

What is the F critical value for (2, 10) at 0.05?

4.10. An F statistic with 2 and 10 degrees of freedom must exceed 4.10 to be significant at the 0.05 level. The same cell at α = 0.01 reads 7.56.

Which degrees of freedom go where?

Numerator df across the top (columns), denominator df down the side (rows). Swapping them changes the value materially — F(2, 10) at 0.05 is 4.10 while F(10, 2) is 19.40 — so check the orientation every time.

Can an F statistic be less than 1?

Yes, and it is common under the null: the numerator variance estimate can easily come out smaller than the denominator's. F below 1 is never significant in the usual (right-tail) test — the interesting action is all in the upper tail.

Why are there separate tables for 0.05 and 0.01?

Tradition from the print era: F needs a two-dimensional grid per α, so books printed only the two standard levels. Software interpolates any α; the two printed levels remain the reporting convention, and both are given here.