Chi-square table

Q: How do you read a chi-square table?

Find the row for your degrees of freedom and the column for your significance level α, which is the area in the right tail. The value where they meet is the critical value. For a test at α = 0.05 with df = 4, the critical value is 9.488: reject the null hypothesis if your chi-square statistic is larger than that.

Q: How do I find the degrees of freedom for a chi-square test?

For a goodness-of-fit test, df = number of categories − 1 (minus one more for each parameter you estimated from the data). For a test of independence or homogeneity in a contingency table, df = (rows − 1) × (columns − 1). A 3 × 4 table has (3 − 1)(4 − 1) = 6 degrees of freedom.

Q: Is a chi-square test one-tailed or two-tailed?

Goodness-of-fit and independence tests are right-tailed: only large chi-square values count as evidence against the null hypothesis, so use the right-tail α columns (0.10, 0.05, 0.01 and so on). The left-tail columns (0.995 to 0.90) are used mainly for confidence intervals and two-sided tests about a variance.

Q: Why are the values in the left columns so small?

Those columns have most of the area (99.5%, 99% …) to the right of the critical value, so the value sits close to zero, at the far left of a right-skewed distribution. With df = 1, only 0.5% of the distribution lies below 0.0000393.

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

The table skips values above 30. Use the lookup at the top of this page, which calculates the exact critical value for any df, including decimals. If you must use the printed table, the next smaller df gives a slightly smaller, less conservative value for right-tail tests, so the exact value is better.

Q: How do I get the p-value instead of a critical value?

Enter your chi-square statistic and degrees of freedom in the p-value calculator and choose chi-square. It gives the exact right-tail p-value with a shaded graph, so you don’t have to bracket it between two table columns.

Find the critical value of chi-square for your degrees of freedom and significance level, from the table or with an exact lookup that explains each step.

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4 Read the result

Critical values of chi-square (area α to the right)

df	0.995	0.99	0.975	0.95	0.9	0.1	0.05	0.025	0.01	0.005
1	0.0000393	0.000157	0.000982	0.00393	0.016	2.706	3.841	5.024	6.635	7.879
2	0.010	0.020	0.051	0.103	0.211	4.605	5.991	7.378	9.210	10.597
3	0.072	0.115	0.216	0.352	0.584	6.251	7.815	9.348	11.345	12.838
4	0.207	0.297	0.484	0.711	1.064	7.779	9.488	11.143	13.277	14.860
5	0.412	0.554	0.831	1.145	1.610	9.236	11.070	12.833	15.086	16.750
6	0.676	0.872	1.237	1.635	2.204	10.645	12.592	14.449	16.812	18.548
7	0.989	1.239	1.690	2.167	2.833	12.017	14.067	16.013	18.475	20.278
8	1.344	1.646	2.180	2.733	3.490	13.362	15.507	17.535	20.090	21.955
9	1.735	2.088	2.700	3.325	4.168	14.684	16.919	19.023	21.666	23.589
10	2.156	2.558	3.247	3.940	4.865	15.987	18.307	20.483	23.209	25.188
11	2.603	3.053	3.816	4.575	5.578	17.275	19.675	21.920	24.725	26.757
12	3.074	3.571	4.404	5.226	6.304	18.549	21.026	23.337	26.217	28.300
13	3.565	4.107	5.009	5.892	7.042	19.812	22.362	24.736	27.688	29.819
14	4.075	4.660	5.629	6.571	7.790	21.064	23.685	26.119	29.141	31.319
15	4.601	5.229	6.262	7.261	8.547	22.307	24.996	27.488	30.578	32.801
16	5.142	5.812	6.908	7.962	9.312	23.542	26.296	28.845	32.000	34.267
17	5.697	6.408	7.564	8.672	10.085	24.769	27.587	30.191	33.409	35.718
18	6.265	7.015	8.231	9.390	10.865	25.989	28.869	31.526	34.805	37.156
19	6.844	7.633	8.907	10.117	11.651	27.204	30.144	32.852	36.191	38.582
20	7.434	8.260	9.591	10.851	12.443	28.412	31.410	34.170	37.566	39.997
21	8.034	8.897	10.283	11.591	13.240	29.615	32.671	35.479	38.932	41.401
22	8.643	9.542	10.982	12.338	14.041	30.813	33.924	36.781	40.289	42.796
23	9.260	10.196	11.689	13.091	14.848	32.007	35.172	38.076	41.638	44.181
24	9.886	10.856	12.401	13.848	15.659	33.196	36.415	39.364	42.980	45.559
25	10.520	11.524	13.120	14.611	16.473	34.382	37.652	40.646	44.314	46.928
26	11.160	12.198	13.844	15.379	17.292	35.563	38.885	41.923	45.642	48.290
27	11.808	12.879	14.573	16.151	18.114	36.741	40.113	43.195	46.963	49.645
28	12.461	13.565	15.308	16.928	18.939	37.916	41.337	44.461	48.278	50.993
29	13.121	14.256	16.047	17.708	19.768	39.087	42.557	45.722	49.588	52.336
30	13.787	14.953	16.791	18.493	20.599	40.256	43.773	46.979	50.892	53.672
40	20.707	22.164	24.433	26.509	29.051	51.805	55.758	59.342	63.691	66.766
50	27.991	29.707	32.357	34.764	37.689	63.167	67.505	71.420	76.154	79.490
60	35.534	37.485	40.482	43.188	46.459	74.397	79.082	83.298	88.379	91.952
70	43.275	45.442	48.758	51.739	55.329	85.527	90.531	95.023	100.425	104.215
80	51.172	53.540	57.153	60.391	64.278	96.578	101.879	106.629	112.329	116.321
90	59.196	61.754	65.647	69.126	73.291	107.565	113.145	118.136	124.116	128.299
100	67.328	70.065	74.222	77.929	82.358	118.498	124.342	129.561	135.807	140.169

Each column heading is the area to the right of the critical value. Right-tailed tests use the columns from 0.10 to 0.005.

How to use the chi-square table

Work out your degrees of freedom: categories − 1 for goodness of fit, or (rows − 1)(columns − 1) for a contingency table.
Choose your significance level α, usually 0.05.
Find the row for your df and the column headed with your α. For df = 4 and α = 0.05, the critical value is 9.488.
Compare: if your chi-square statistic is greater than the critical value, reject the null hypothesis.
For values not in the table, or for left-tail and two-tailed cutoffs, use the lookup above. It also highlights the matching cell.

What the chi-square critical value means

The chi-square distribution is right-skewed and only takes positive values. The critical value is the point that leaves an area α in the right tail:

P(χ² > χ²_{α, df}) = α

The test statistic it is compared with, for goodness of fit or independence, is

χ² = Σ (O − E)²E

χ²: The chi-square statistic calculated from your data
O, E: Observed and expected counts in each category or cell
α: The significance level: the area in the right tail beyond the critical value
df: Degrees of freedom, which set the shape of the distribution; larger df shifts it to the right

Worked example

A store expects customers to be spread evenly across its 5 weekdays. Over one week it counts 18, 22, 30, 16 and 14 customers (100 in total). Is that consistent with an even spread, at α = 0.05?

Expected count per day if the spread is even
E = 1005 = 20
Chi-square statistic
χ² = (18−20)² + (22−20)² + (30−20)² + (16−20)² + (14−20)²20 = 16020 = 8.0
df = 5 − 1 = 4; table row 4, column 0.05
χ²_{0.05, 4} = 9.488
Compare
8.0 < 9.488 → fail to reject H₀

What it means: the busiest day had 30 customers, but with only 100 customers in total that much variation could easily happen by chance. The data don't give strong evidence that some days are busier than others.

Tips for using the chi-square table

Bigger statistic, stronger evidence. Unlike z and t, the chi-square statistic is never negative, and large values mean the data don't fit the null hypothesis.
Check expected counts. The test is reliable when every expected count is at least 5. Combine sparse categories if they aren't.
For a variance confidence interval, use both a left-tail and a right-tail value: choose "Both tails" in the lookup to get the pair.
Need an exact p-value? The p-value calculator gives it directly, and the critical value calculator covers z, t and F as well.

Frequently asked questions

How do you read a chi-square table?

Find the row for your degrees of freedom and the column for your significance level α, which is the area in the right tail. The value where they meet is the critical value. For a test at α = 0.05 with df = 4, the critical value is 9.488: reject the null hypothesis if your chi-square statistic is larger than that.

How do I find the degrees of freedom for a chi-square test?

For a goodness-of-fit test, df = number of categories − 1 (minus one more for each parameter you estimated from the data). For a test of independence or homogeneity in a contingency table, df = (rows − 1) × (columns − 1). A 3 × 4 table has (3 − 1)(4 − 1) = 6 degrees of freedom.

Is a chi-square test one-tailed or two-tailed?

Goodness-of-fit and independence tests are right-tailed: only large chi-square values count as evidence against the null hypothesis, so use the right-tail α columns (0.10, 0.05, 0.01 and so on). The left-tail columns (0.995 to 0.90) are used mainly for confidence intervals and two-sided tests about a variance.

Why are the values in the left columns so small?

Those columns have most of the area (99.5%, 99% …) to the right of the critical value, so the value sits close to zero, at the far left of a right-skewed distribution. With df = 1, only 0.5% of the distribution lies below 0.0000393.

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

The table skips values above 30. Use the lookup at the top of this page, which calculates the exact critical value for any df, including decimals. If you must use the printed table, the next smaller df gives a slightly smaller, less conservative value for right-tail tests, so the exact value is better.

How do I get the p-value instead of a critical value?

Enter your chi-square statistic and degrees of freedom in the p-value calculator and choose chi-square. It gives the exact right-tail p-value with a shaded graph, so you don’t have to bracket it between two table columns.

Last reviewed November 11, 2026

Critical values of chi-square (area α to the right)

How to use the chi-square table

What the chi-square critical value means

Worked example

Tips for using the chi-square table

Frequently asked questions

How do you read a chi-square table?

How do I find the degrees of freedom for a chi-square test?

Is a chi-square test one-tailed or two-tailed?

Why are the values in the left columns so small?

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

How do I get the p-value instead of a critical value?

Related tools

P-value calculator

Critical value calculator

T-table (critical values)

Z-table (standard normal table)