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F-table (critical values for ANOVA and regression)

Critical values of the F distribution at the two standard significance levels, plus an exact lookup for any df1/df2 pair — no more interpolating between printed columns.

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Exact F lookup

Any df1/df2 pair and α — exact critical value and p-value.

Significance level

Numerator df (df1)

Denominator df (df2)

F value (optional)

Critical values of F at α = .05

Numerator df (df1, between groups) across the top; denominator df (df2, within groups / error) down the side.

df2 \ df1	1	2	3	4	5	6	7	8	10	12	15	20	30
1	161.4	199.5	215.7	224.6	230.2	234.0	236.8	238.9	241.9	243.9	245.9	248.0	250.1
2	18.51	19.00	19.16	19.25	19.30	19.33	19.35	19.37	19.40	19.41	19.43	19.45	19.46
3	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.79	8.74	8.70	8.66	8.62
4	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	5.96	5.91	5.86	5.80	5.75
5	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.74	4.68	4.62	4.56	4.50
6	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.06	4.00	3.94	3.87	3.81
7	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.64	3.57	3.51	3.44	3.38
8	5.32	4.46	4.07	3.84	3.69	3.58	3.50	3.44	3.35	3.28	3.22	3.15	3.08
9	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.14	3.07	3.01	2.94	2.86
10	4.96	4.10	3.71	3.48	3.33	3.22	3.14	3.07	2.98	2.91	2.85	2.77	2.70
12	4.75	3.89	3.49	3.26	3.11	3.00	2.91	2.85	2.75	2.69	2.62	2.54	2.47
14	4.60	3.74	3.34	3.11	2.96	2.85	2.76	2.70	2.60	2.53	2.46	2.39	2.31
16	4.49	3.63	3.24	3.01	2.85	2.74	2.66	2.59	2.49	2.42	2.35	2.28	2.19
18	4.41	3.55	3.16	2.93	2.77	2.66	2.58	2.51	2.41	2.34	2.27	2.19	2.11
20	4.35	3.49	3.10	2.87	2.71	2.60	2.51	2.45	2.35	2.28	2.20	2.12	2.04
25	4.24	3.39	2.99	2.76	2.60	2.49	2.40	2.34	2.24	2.16	2.09	2.01	1.92
30	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.16	2.09	2.01	1.93	1.84
40	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.08	2.00	1.92	1.84	1.74
60	4.00	3.15	2.76	2.53	2.37	2.25	2.17	2.10	1.99	1.92	1.84	1.75	1.65
120	3.92	3.07	2.68	2.45	2.29	2.18	2.09	2.02	1.91	1.83	1.75	1.66	1.55

Reject H0 when F exceeds the table value. For a one-way ANOVA with k groups and N total participants: df1 = k − 1, df2 = N − k.

Critical values of F at α = .01

Numerator df (df1, between groups) across the top; denominator df (df2, within groups / error) down the side.

df2 \ df1	1	2	3	4	5	6	7	8	10	12	15	20	30
1	4052.2	4999.5	5403.4	5624.6	5763.6	5859.0	5928.4	5981.1	6055.8	6106.3	6157.3	6208.7	6260.6
2	98.50	99.00	99.17	99.25	99.30	99.33	99.36	99.37	99.40	99.42	99.43	99.45	99.47
3	34.12	30.82	29.46	28.71	28.24	27.91	27.67	27.49	27.23	27.05	26.87	26.69	26.50
4	21.20	18.00	16.69	15.98	15.52	15.21	14.98	14.80	14.55	14.37	14.20	14.02	13.84
5	16.26	13.27	12.06	11.39	10.97	10.67	10.46	10.29	10.05	9.89	9.72	9.55	9.38
6	13.75	10.92	9.78	9.15	8.75	8.47	8.26	8.10	7.87	7.72	7.56	7.40	7.23
7	12.25	9.55	8.45	7.85	7.46	7.19	6.99	6.84	6.62	6.47	6.31	6.16	5.99
8	11.26	8.65	7.59	7.01	6.63	6.37	6.18	6.03	5.81	5.67	5.52	5.36	5.20
9	10.56	8.02	6.99	6.42	6.06	5.80	5.61	5.47	5.26	5.11	4.96	4.81	4.65
10	10.04	7.56	6.55	5.99	5.64	5.39	5.20	5.06	4.85	4.71	4.56	4.41	4.25
12	9.33	6.93	5.95	5.41	5.06	4.82	4.64	4.50	4.30	4.16	4.01	3.86	3.70
14	8.86	6.51	5.56	5.04	4.69	4.46	4.28	4.14	3.94	3.80	3.66	3.51	3.35
16	8.53	6.23	5.29	4.77	4.44	4.20	4.03	3.89	3.69	3.55	3.41	3.26	3.10
18	8.29	6.01	5.09	4.58	4.25	4.01	3.84	3.71	3.51	3.37	3.23	3.08	2.92
20	8.10	5.85	4.94	4.43	4.10	3.87	3.70	3.56	3.37	3.23	3.09	2.94	2.78
25	7.77	5.57	4.68	4.18	3.85	3.63	3.46	3.32	3.13	2.99	2.85	2.70	2.54
30	7.56	5.39	4.51	4.02	3.70	3.47	3.30	3.17	2.98	2.84	2.70	2.55	2.39
40	7.31	5.18	4.31	3.83	3.51	3.29	3.12	2.99	2.80	2.66	2.52	2.37	2.20
60	7.08	4.98	4.13	3.65	3.34	3.12	2.95	2.82	2.63	2.50	2.35	2.20	2.03
120	6.85	4.79	3.95	3.48	3.17	2.96	2.79	2.66	2.47	2.34	2.19	2.03	1.86

Reject H0 when F exceeds the table value. For a one-way ANOVA with k groups and N total participants: df1 = k − 1, df2 = N − k.

How to read the table

An F statistic is a ratio of variances, so it carries TWO degrees of freedom: the numerator df1 (across the top) and the denominator df2 (down the side). Find your α table, then the intersection. Example: a one-way ANOVA with 3 groups of 20 has df1 = 3 − 1 = 2 and df2 = 60 − 3 = 57; at α = .05 the critical value is about 3.16, so F(2, 57) = 4.4 is significant.

In regression, the overall model F uses df1 = number of predictors and df2 = n − predictors − 1. In ANOVA the same logic extends to each effect in a factorial design — each has its own df1 against the common error df2.

A significant F in an ANOVA with 3+ groups says only that SOME difference exists. Follow up with planned contrasts or post-hoc tests to find where, and report an effect size (η² or ω²) alongside.

Frequently asked questions

Which df is the numerator and which is the denominator?

Numerator (df1) belongs to the effect: groups − 1 in a one-way ANOVA, or the number of predictors in a regression F. Denominator (df2) belongs to the error term: N − k for one-way ANOVA, n − p − 1 in regression. Reporting convention: F(df1, df2) = value.

Why is F always one-tailed?

F is a ratio of squared quantities, so any group difference — in either direction — inflates it above 1. All the evidence against H0 collects in the upper tail; that is the only tail tested.

My exact df2 is not printed — which row do I use?

The exact lookup at the top takes any df pair. On paper, use the next SMALLER df2 (a slightly larger critical value, so the choice is conservative).

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