Chi-Square Table

Chi-square critical values and p-values by degrees of freedom, with reverse lookup.

FreeNo accountOn your device

Runs in your browser. How to verify

Loading tool…

Full printable reference table

Chi-square critical values
df	α = 0.1	α = 0.05	α = 0.025	α = 0.01	α = 0.005	α = 0.001
1	2.706	3.841	5.024	6.635	7.879	10.828
2	4.605	5.991	7.378	9.210	10.597	13.816
3	6.251	7.815	9.348	11.345	12.838	16.266
4	7.779	9.488	11.143	13.277	14.860	18.467
5	9.236	11.070	12.833	15.086	16.750	20.515
6	10.645	12.592	14.449	16.812	18.548	22.458
7	12.017	14.067	16.013	18.475	20.278	24.322
8	13.362	15.507	17.535	20.090	21.955	26.124
9	14.684	16.919	19.023	21.666	23.589	27.877
10	15.987	18.307	20.483	23.209	25.188	29.588
11	17.275	19.675	21.920	24.725	26.757	31.264
12	18.549	21.026	23.337	26.217	28.300	32.909
13	19.812	22.362	24.736	27.688	29.819	34.528
14	21.064	23.685	26.119	29.141	31.319	36.123
15	22.307	24.996	27.488	30.578	32.801	37.697
16	23.542	26.296	28.845	32.000	34.267	39.252
17	24.769	27.587	30.191	33.409	35.718	40.790
18	25.989	28.869	31.526	34.805	37.156	42.312
19	27.204	30.144	32.852	36.191	38.582	43.820
20	28.412	31.410	34.170	37.566	39.997	45.315
22	30.813	33.924	36.781	40.289	42.796	48.268
24	33.196	36.415	39.364	42.980	45.559	51.179
26	35.563	38.885	41.923	45.642	48.290	54.052
28	37.916	41.337	44.461	48.278	50.993	56.892
30	40.256	43.773	46.979	50.892	53.672	59.703
40	51.805	55.758	59.342	63.691	66.766	73.402
50	63.167	67.505	71.420	76.154	79.490	86.661
60	74.397	79.082	83.298	88.379	91.952	99.607
80	96.578	101.879	106.629	112.329	116.321	124.839
100	118.498	124.342	129.561	135.807	140.169	149.449

About this tool

Enter degrees of freedom and alpha for a right-tailed chi-square cut-off, or enter a chi-square statistic to get its p-value.

How to use

Step 1

Choose critical value or p-value.

Step 2

Enter df and alpha, or df and the statistic.

Step 3

Pick right or left tail and press Calculate.

How it works

Chi-square tests are almost always right-tailed: a large statistic means observed counts are far from expected. The shape is skewed for small df and approaches normal as df grows. For goodness-of-fit df = categories − 1; for a contingency table df = (rows − 1)(columns − 1).

Reject H₀ when χ² > χ²(α, df)

Worked example

df = 10 at 5%

Input: Critical value, df = 10, α = 0.05, right tail
Output: 18.307
Walkthrough: Only 5% of the chi-square(10) distribution lies above 18.307. Entering χ² = 18.307 gives p = 0.0500.

Limitations

Table values are exact, not rounded.
Needs expected counts of about 5 or more for the test to be valid.

Questions

What is the chi-square critical value for df 10 at 0.05?

18.307.

What is it for df 5?

11.070 at α = 0.05.

How do I get df for a contingency table?

(rows − 1) × (columns − 1).

Features

Critical and p-value
Right and left tail
Runs in your browser

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

P-values and significance tests
Khan Academy
How critical values and p-values connect on Statistics Hub.
Watch on YouTube
Hypothesis testing and p-values
StatQuest with Josh Starmer
Intuition for t/z/χ² decision rules.
Watch on YouTube

Introductory Statistics
OpenStax
Free textbook for hypothesis tests and tables.
STAT online programs
Penn State
University stats notes for tests and distributions.

More Statistics tools

See all ›

Chi-Square Distribution Calculator

Chi-square density, cumulative probability, and quantile for any degrees of freedom.

Chi-Square Goodness-of-Fit Test

Chi-square goodness-of-fit test comparing observed counts to an expected distribution.

Chi-Square Test of Independence

Chi-square test of independence on a contingency table with Cramer's V.

Chi-Square Calculator

Chi-square goodness-of-fit statistic.