Chi-Squared Critical Values Table

The chi-squared table shows critical values χ²* for right-tail hypothesis tests. For a given degrees of freedom (df) and significance level α, the cell gives the value where P(χ² > χ²*) = α.

These values are used in goodness-of-fit tests, tests of independence, and variance tests. Hover a cell to see the rejection region on the companion chart.

df \ α (right tail)	0.1	0.05	0.025	0.01	0.005
1	2.7055	3.8415	5.0239	6.6349	7.8794
2	4.6052	5.9915	7.3778	9.2103	10.5966
3	6.2514	7.8147	9.3484	11.3449	12.8382
4	7.7794	9.4877	11.1433	13.2767	14.8603
5	9.2364	11.0705	12.8325	15.0863	16.7496
6	10.6446	12.5916	14.4494	16.8119	18.5476
7	12.0170	14.0671	16.0128	18.4753	20.2777
8	13.3616	15.5073	17.5345	20.0902	21.9550
9	14.6837	16.9190	19.0228	21.6660	23.5894
10	15.9872	18.3070	20.4832	23.2093	25.1882
11	17.2750	19.6751	21.9200	24.7250	26.7568
12	18.5493	21.0261	23.3367	26.2170	28.2995
13	19.8119	22.3620	24.7356	27.6882	29.8195
14	21.0641	23.6848	26.1189	29.1412	31.3193
15	22.3071	24.9958	27.4884	30.5779	32.8013
16	23.5418	26.2962	28.8454	31.9999	34.2672
17	24.7690	27.5871	30.1910	33.4087	35.7185
18	25.9894	28.8693	31.5264	34.8053	37.1565
19	27.2036	30.1435	32.8523	36.1909	38.5823
20	28.4120	31.4104	34.1696	37.5662	39.9968
21	29.6151	32.6706	35.4789	38.9322	41.4011
22	30.8133	33.9244	36.7807	40.2894	42.7957
23	32.0069	35.1725	38.0756	41.6384	44.1813
24	33.1962	36.4150	39.3641	42.9798	45.5585
25	34.3816	37.6525	40.6465	44.3141	46.9279
26	35.5632	38.8851	41.9232	45.6417	48.2899
27	36.7412	40.1133	43.1945	46.9629	49.6449
28	37.9159	41.3371	44.4608	48.2782	50.9934
29	39.0875	42.5570	45.7223	49.5879	52.3356
30	40.2560	43.7730	46.9792	50.8922	53.6720
40	51.8051	55.7585	59.3417	63.6907	66.7660
50	63.1671	67.5048	71.4202	76.1539	79.4900
60	74.3970	79.0819	83.2977	88.3794	91.9517
80	96.5782	101.8795	106.6286	112.3288	116.3211
100	118.4980	124.3421	129.5612	135.8067	140.1695

Distribution Curve

How to Use

Calculate your degrees of freedom from the test setup
Choose your significance level α (commonly 0.05)
Find the critical value χ²* at the intersection
Reject H₀ if your test statistic > χ²*

Explore this distribution interactively:

Open Chi-Squared Distribution →

Frequently Asked Questions

What is the chi-squared table used for?

It provides critical values for chi-squared tests: goodness-of-fit tests, tests of independence in contingency tables, and tests about population variance.

How do I determine the degrees of freedom?

For a goodness-of-fit test, df = (number of categories) − 1. For a test of independence, df = (rows − 1)(columns − 1).

Why does the chi-squared distribution only have a right tail?

Chi-squared values are always non-negative (they're sums of squared values). Most tests check if the observed statistic is too large, hence right-tailed.