F Table: Critical Values of the F Distribution (alpha = 0.05)

An F table lists the upper critical values of the F distribution: the cut-off an F statistic must exceed for a one-sided test to reject the null hypothesis at a chosen significance level. The table below gives the α = 0.05 values for numerator degrees of freedom 1 to 10 and 35 denominator degrees of freedom rows, copied from the NIST/SEMATECH e-Handbook. Look up your two degrees of freedom, compare your F statistic, and reject only if it is larger than the tabled value.

How to read the F table

Columns are the numerator degrees of freedom (ν₁, written df1 below) and rows are the denominator degrees of freedom (ν₂, df2). The cell at their intersection is the critical value F_0.05(ν₁, ν₂). NIST states the rule plainly: for a one-sided test, the null hypothesis is rejected when the test statistic is greater than the tabled value.

Printed tables are not laid out the same way everywhere, and some swap rows and columns, so check which axis is numerator before you read a value. The order matters because the two degrees of freedom are not interchangeable: the table gives 19.247 for df1 = 4 and df2 = 2, but 6.944 for df1 = 2 and df2 = 4. In ANOVA, df1 is the between-groups df and df2 the within-groups (error) df; our guide to the F-statistic in ANOVA and regression shows where each comes from.

F table (alpha = 0.05) critical values

Upper-tail critical values, one-sided, 5% significance level. Source: NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.6.7.3, read 2026-10-29. Values are shown to three decimal places exactly as NIST prints them; they are rounded, so a computed F that matches the tabled value to three decimals is a boundary case worth checking with software. The full NIST table runs df2 from 1 to 100 and also covers the 10% and 1% levels and df1 11 to 20.

df2 df1	1	2	3	4	5	6	7	8	9	10
1	161.448	199.500	215.707	224.583	230.162	233.986	236.768	238.882	240.543	241.882
2	18.513	19.000	19.164	19.247	19.296	19.330	19.353	19.371	19.385	19.396
3	10.128	9.552	9.277	9.117	9.013	8.941	8.887	8.845	8.812	8.786
4	7.709	6.944	6.591	6.388	6.256	6.163	6.094	6.041	5.999	5.964
5	6.608	5.786	5.409	5.192	5.050	4.950	4.876	4.818	4.772	4.735
6	5.987	5.143	4.757	4.534	4.387	4.284	4.207	4.147	4.099	4.060
7	5.591	4.737	4.347	4.120	3.972	3.866	3.787	3.726	3.677	3.637
8	5.318	4.459	4.066	3.838	3.687	3.581	3.500	3.438	3.388	3.347
9	5.117	4.256	3.863	3.633	3.482	3.374	3.293	3.230	3.179	3.137
10	4.965	4.103	3.708	3.478	3.326	3.217	3.135	3.072	3.020	2.978
11	4.844	3.982	3.587	3.357	3.204	3.095	3.012	2.948	2.896	2.854
12	4.747	3.885	3.490	3.259	3.106	2.996	2.913	2.849	2.796	2.753
13	4.667	3.806	3.411	3.179	3.025	2.915	2.832	2.767	2.714	2.671
14	4.600	3.739	3.344	3.112	2.958	2.848	2.764	2.699	2.646	2.602
15	4.543	3.682	3.287	3.056	2.901	2.790	2.707	2.641	2.588	2.544
16	4.494	3.634	3.239	3.007	2.852	2.741	2.657	2.591	2.538	2.494
17	4.451	3.592	3.197	2.965	2.810	2.699	2.614	2.548	2.494	2.450
18	4.414	3.555	3.160	2.928	2.773	2.661	2.577	2.510	2.456	2.412
19	4.381	3.522	3.127	2.895	2.740	2.628	2.544	2.477	2.423	2.378
20	4.351	3.493	3.098	2.866	2.711	2.599	2.514	2.447	2.393	2.348
21	4.325	3.467	3.072	2.840	2.685	2.573	2.488	2.420	2.366	2.321
22	4.301	3.443	3.049	2.817	2.661	2.549	2.464	2.397	2.342	2.297
23	4.279	3.422	3.028	2.796	2.640	2.528	2.442	2.375	2.320	2.275
24	4.260	3.403	3.009	2.776	2.621	2.508	2.423	2.355	2.300	2.255
25	4.242	3.385	2.991	2.759	2.603	2.490	2.405	2.337	2.282	2.236
26	4.225	3.369	2.975	2.743	2.587	2.474	2.388	2.321	2.265	2.220
27	4.210	3.354	2.960	2.728	2.572	2.459	2.373	2.305	2.250	2.204
28	4.196	3.340	2.947	2.714	2.558	2.445	2.359	2.291	2.236	2.190
29	4.183	3.328	2.934	2.701	2.545	2.432	2.346	2.278	2.223	2.177
30	4.171	3.316	2.922	2.690	2.534	2.421	2.334	2.266	2.211	2.165
40	4.085	3.232	2.839	2.606	2.449	2.336	2.249	2.180	2.124	2.077
50	4.034	3.183	2.790	2.557	2.400	2.286	2.199	2.130	2.073	2.026
60	4.001	3.150	2.758	2.525	2.368	2.254	2.167	2.097	2.040	1.993
80	3.960	3.111	2.719	2.486	2.329	2.214	2.126	2.056	1.999	1.951
100	3.936	3.087	2.696	2.463	2.305	2.191	2.103	2.032	1.975	1.927

The F distribution formula

The F distribution is the ratio of two chi-square distributions with degrees of freedom ν₁ and ν₂; as the R documentation puts it, each chi-squared variate is divided by its degrees of freedom. NIST gives its probability density function, for x > 0, as:

f(x) = Γ((ν1+ν2)/2) (ν1/ν2)ν1/2 xν1/2 − 1 / [ Γ(ν1/2) Γ(ν2/2) (1 + ν1x/ν2)(ν1+ν2)/2 ]

A critical value F_α(ν₁, ν₂) is the point that leaves probability α in the upper tail of this density. Because the distribution is asymmetric and takes only positive values, NIST notes that a two-sided test needs a separate set of tables covering both tails; this one-sided table does not provide them. For the logic of choosing a tail, see one-tailed vs two-tailed tests.

Worked example 1: one-way ANOVA

Suppose a study compares 3 groups with 23 observations in total. Then df1 = 3 − 1 = 2 and df2 = 23 − 3 = 20. The table gives F_0.05(2, 20) = 3.493. If the ANOVA output reports a (hypothetical) F = 4.2, that exceeds 3.493, so you reject the null hypothesis of equal group means at the 0.05 level. If it reports F = 2.9, it does not.

Worked example 2: comparing two variances

NIST lists testing whether the variances of two populations are equal among the uses of the F distribution. Suppose the numerator sample has 6 observations (df1 = 5) and the denominator sample has 11 (df2 = 10). The table gives F_0.05(5, 10) = 3.326. A (hypothetical) variance ratio of 4.1 is larger than 3.326, so the one-sided test rejects equal variances at the 5% level. Remember that this is a one-sided comparison; a two-sided variance test needs the lower-tail values that this table omits.

Compute F critical values in Excel, R and Python

Software removes the need for a table and covers any degrees of freedom, including those the printed grid skips. All three below return the upper critical value for significance level alpha.

Excel

=F.INV.RT(0.05, 2, 20) returns the inverse of the right-tailed F distribution: probability, then numerator df, then denominator df (Microsoft Support, F.INV.RT function, read 2026-10-29). It should return the 3.493 shown above, to rounding.

R

qf(1 - 0.05, df1 = 2, df2 = 20) or equivalently qf(0.05, 2, 20, lower.tail = FALSE). In the R stats documentation, lower.tail = TRUE (the default) gives P[X ≤ x], so the upper critical value needs either 1 − alpha or lower.tail = FALSE.

Python

from scipy.stats import f then f.ppf(1 - 0.05, dfn=2, dfd=20). In SciPy, dfn is the numerator and dfd the denominator degrees of freedom, and ppf is the percent point function, the inverse of the cdf. For a full ANOVA workflow in Python, see ANOVA in Python with statsmodels. To turn an F statistic into a p-value instead, see the p-value entry; for z, t and chi-square lookups, see how to find a critical value.

F table PDF: print or save

To keep an F table as a PDF, use your browser’s print dialog on this page and choose Save as PDF; the table is plain text, so it stays searchable and copyable. The values come from the NIST Handbook page cited above, which you can also cite directly in a methods section.

FAQ

What does the F table give you?

The upper critical value of the F distribution for a chosen alpha and a pair of degrees of freedom. Reject the null hypothesis in a one-sided test when your F statistic is greater than it.

Which degrees of freedom go on the rows and columns?

In the NIST table used here, columns are numerator df (ν₁) and rows are denominator df (ν₂). Other tables may reverse this, so check the labels.

Is the F table for one-tailed or two-tailed tests?

This table is for one-sided tests, with alpha entirely in the upper tail. Two-sided tests need tables with both tails, which NIST does not include.

What if my degrees of freedom are not in the table?

Compute the exact critical value with F.INV.RT in Excel, qf in R or scipy.stats.f.ppf in Python, as shown above.