Critical Values for Chi Square Distribution Table

The Chi Square Table gives you critical values for the chi-square distribution. Use it to decide if your calculated chi-square statistic is significant in hypothesis testing.

Students, teachers, and researchers rely on this table for goodness-of-fit tests, tests of independence, and variance analysis. Find critical values quickly by degrees of freedom and significance level (alpha).

What Is a Chi Square Table?

A Chi Square Table lists critical values for the chi-square distribution. These values help you decide if your test results are statistically significant.

The chi-square distribution is used when you compare observed data to expected data. It is always positive and skewed to the right.

Real-world example
In a survey, you expect equal votes for three options. After collecting data, you calculate a chi-square statistic. The table tells you if the difference is due to chance or real preference.

This table is essential for chi-square goodness-of-fit tests and tests of independence in statistics.

How to Use a Chi Square Table

A Chi Square Table gives critical values for the right tail of the chi-square distribution. Use it to compare your calculated chi-square statistic to the table value.

Step 1: Calculate the degrees of freedom (df). For goodness-of-fit: df = number of categories − 1. For test of independence: df = (rows − 1) × (columns − 1).

Step 2: Choose your significance level (alpha). Common choices: 0.05 or 0.01.

Step 3: Find the row for your df in the left column.

Step 4: Move across to the column for your alpha (example: 0.05). Step 5: Read the number in that cell. This is your critical value.

Step 6: Compare: If your calculated chi-square > critical value, reject the null hypothesis.

The table shows right-tail probabilities only. For most tests, this is what you need.

Chi Square Critical Value Table

df	0.2	0.1	0.05	0.04	0.03	0.025	0.02	0.01	0.005	0.0005
1	1.642	2.706	3.841	4.218	4.709	5.024	5.412	6.635	7.879	12.116
2	3.219	4.605	5.991	6.424	6.962	7.378	7.824	9.210	10.597	15.202
3	4.642	6.251	7.815	8.292	8.883	9.348	9.837	11.345	12.838	17.731
4	5.989	7.779	9.488	10.001	10.633	11.143	11.668	13.277	14.860	20.092
5	7.289	9.236	11.070	11.618	12.295	12.833	13.388	15.086	16.750	22.307
6	8.558	10.645	12.592	13.175	13.892	14.449	15.033	16.812	18.548	24.433
7	9.803	12.017	14.067	14.681	15.432	16.013	16.622	18.475	20.278	26.510
8	11.030	13.362	15.507	16.151	16.936	17.535	18.168	20.090	21.955	28.560
9	12.242	14.684	16.919	17.591	18.406	19.023	19.679	21.666	23.589	30.585
10	13.442	15.987	18.307	19.005	19.851	20.483	21.161	23.209	25.188	32.591
11	14.631	17.275	19.675	20.399	21.273	21.920	22.618	24.725	26.757	34.582
12	15.812	18.549	21.026	21.774	22.676	23.337	24.054	26.217	28.300	36.561
13	16.985	19.812	22.362	23.133	24.062	24.736	25.472	27.688	29.819	38.528
14	18.151	21.064	23.685	24.478	25.434	26.119	26.873	29.141	31.319	40.484
15	19.311	22.307	24.996	25.812	26.794	27.488	28.259	30.578	32.801	42.431
16	20.465	23.542	26.296	27.133	28.141	28.845	29.633	32.000	34.267	44.370
17	21.615	24.769	27.587	28.445	29.477	30.191	30.995	33.409	35.718	46.301
18	22.760	25.989	28.869	29.747	30.803	31.526	32.346	34.805	37.156	48.225
19	23.900	27.204	30.144	31.042	32.123	32.852	33.687	36.191	38.582	50.143
20	25.038	28.412	31.410	32.328	33.437	34.170	35.020	37.566	39.997	52.056
21	26.171	29.615	32.671	33.607	34.742	35.479	36.343	38.932	41.401	53.964
22	27.301	30.813	33.924	34.878	36.042	36.781	37.659	40.289	42.796	55.868
23	28.429	32.007	35.172	36.142	37.338	38.076	38.968	41.638	44.181	57.767
24	29.553	33.196	36.415	37.401	38.629	39.364	40.270	42.980	45.559	59.663
25	30.675	34.382	37.652	38.655	39.915	40.646	41.566	44.314	46.928	61.554
26	31.795	35.563	38.885	39.904	41.197	41.923	42.858	45.642	48.290	63.442
27	32.912	36.741	40.113	41.149	42.475	43.195	44.145	46.963	49.645	65.327
28	34.027	37.916	41.337	42.390	43.749	44.461	45.427	48.278	50.993	67.208
29	35.139	39.087	42.557	43.627	45.019	45.722	46.704	49.588	52.336	69.086
30	36.250	40.256	43.773	44.860	46.285	46.979	47.976	50.892	53.672	70.961
31	37.358	41.422	44.985	46.089	47.547	48.232	49.243	52.191	55.003	72.832
32	38.465	42.585	46.194	47.315	48.805	49.480	50.506	53.486	56.328	74.700
33	39.569	43.745	47.400	48.537	50.060	50.725	51.766	54.776	57.648	76.565
34	40.672	44.903	48.602	49.756	51.311	51.966	53.021	56.061	58.964	78.427
35	41.772	46.059	49.802	50.972	52.559	53.203	54.273	57.342	60.275	80.286
40	46.979	51.805	55.758	56.943	58.365	59.342	60.436	63.691	66.766	88.379
45	52.106	57.505	61.656	62.902	64.401	65.410	66.554	69.957	73.166	96.217
50	57.153	63.167	67.505	68.796	70.364	71.420	72.613	76.154	79.490	103.875
55	62.129	68.796	73.311	74.645	76.270	77.380	78.611	82.292	85.749	111.398
60	67.053	74.397	79.082	80.457	82.138	83.298	84.580	88.379	91.952	118.786
65	71.931	79.973	84.821	86.237	87.975	89.177	90.498	94.422	98.105	126.032
70	76.764	85.527	90.531	91.988	93.785	95.023	96.383	100.425	104.215	133.136
75	81.562	91.057	96.217	97.715	99.570	100.839	102.238	106.393	110.286	140.109
80	86.329	96.578	101.879	103.418	105.330	106.629	108.066	112.329	116.321	146.955
85	91.061	102.079	107.522	109.102	111.070	112.399	113.874	118.136	122.271	153.669
90	95.758	107.565	113.145	114.766	116.791	118.136	119.647	124.116	128.299	160.251
95	100.422	113.038	118.752	120.414	122.495	123.858	125.396	129.973	134.300	166.701
100	105.053	118.498	124.342	126.035	128.164	129.561	131.126	135.807	140.169	173.022

Chi Square Table Examples

These examples show how to use the chi square table to find critical values and interpret test results.

Example 1: Goodness-of-fit test (two categories)

You roll a die 60 times. You expect each face to appear 10 times. Calculated chi-square = 8.4. Degrees of freedom: df = 6 − 1 = 5. Significance level: alpha = 0.05.

Look in row df=5, column alpha=0.05. Critical value ≈ 11.070.

Since 8.4 < 11.070, fail to reject the null hypothesis. The die appears fair.

Example 2: Test of independence (2×3 table)

You survey 200 people on preferred drink by age group. Calculated chi-square = 12.6. df = (2−1) × (3−1) = 2. Alpha = 0.01.

Row df=2, column alpha=0.01. Critical value ≈ 9.210.

Since 12.6 > 9.210, reject the null hypothesis. Preference depends on age group.

Example 3: Small sample variance test

You test if population variance equals 25 using n=10 observations. Calculated chi-square = 18.2. df = 10 − 1 = 9. Alpha = 0.05 (two-tailed test).

For two-tailed, use alpha/2 = 0.025 for upper tail. Critical value (upper) ≈ 19.023. Lower critical value ≈ 2.700 (from alpha=0.975 column if available, or note symmetry).

Since 18.2 is between lower and upper, fail to reject the null.

Use these steps to apply the chi square table in your own problems.

Common Mistakes When Using a Chi Square Table

Many people make these errors when reading a chi square table. Avoid them for accurate hypothesis testing.

• Using the wrong degrees of freedom. Always calculate df correctly: categories − 1 for goodness-of-fit, (rows − 1) × (columns − 1) for independence.
• Looking at the wrong tail. The standard chi square table shows right-tail critical values. Most tests need the upper tail.
• Choosing the wrong alpha level. Use 0.05 or 0.01 as specified in your problem. Do not mix them.
• Forgetting two-tailed adjustments. For two-tailed tests (rare in chi-square), split alpha (use alpha/2 for each tail).
• Misreading the row or column. Double-check the df row and alpha column before taking the value.
• Comparing the wrong way. Reject the null only if calculated chi-square is greater than the critical value (not less).

Review these points before you finish any chi-square test.

Explore More Statistics Calculators

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