About Chi-Square Critical Value Table
This chi-square critical value table lists the right-tail critical values for 1 to 30 degrees of freedom at the common significance levels, and the calculator above finds the value for any other degrees of freedom or alpha. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Reject the null hypothesis when your chi-square statistic is larger than the value in the table for your degrees of freedom and significance level. Every value in the table is computed by the same code as the calculator, and it matches printed tables such as the one in the NIST/SEMATECH e-Handbook, for example 3.841 for 1 degree of freedom and 18.307 for 10 degrees of freedom at 0.05.
Use the look-up mode for a degree of freedom or alpha that is not in the table, for example df = 7.5 or alpha = 0.02. The curve shades the right tail so you can see what the critical value cuts off.
How to use Chi-Square Critical Value Table
- Choose the test: goodness of fit, independence or critical value.
- For goodness of fit, type the observed counts and choose how the expected values are given. For independence, type the counts into the table and add or remove rows and columns as needed.
- Choose a significance level, usually 0.05.
- Read the chi-square statistic, the degrees of freedom, the p-value, the critical value and, for a table, Cramér’s V.
- Check the warning about small expected counts, then open the expected counts, contributions and step-by-step working.
Features
- Goodness of fit with equal, proportional or custom expected values, and an option for estimated parameters.
- Test of independence with an editable contingency table up to 10 by 10, usable on a phone.
- Expected counts and each cell’s contribution to chi-square.
- Cramér’s V effect size with a plain-language label.
- A warning when any expected count is under 5.
- Critical value look-up for any degrees of freedom and significance level.
- A bell curve with the rejection region and statistic, and step-by-step KaTeX working.
What the critical value is
It is the point that leaves area alpha to its right under the chi-square curve with the given degrees of freedom.
P(χ²_df ≥ χ²_c) = αWorked examples
df = 1, α = 0.05 gives critical value 3.841
df = 10, α = 0.05 gives critical value 18.31
df = 5, α = 0.01 gives critical value 15.09
Chi-square critical values by degrees of freedom
| df | α = 0.10 | α = 0.05 | α = 0.025 | α = 0.01 | α = 0.001 |
|---|---|---|---|---|---|
| 1 | 2.706 | 3.841 | 5.024 | 6.635 | 10.83 |
| 2 | 4.605 | 5.991 | 7.378 | 9.21 | 13.82 |
| 3 | 6.251 | 7.815 | 9.348 | 11.34 | 16.27 |
| 4 | 7.779 | 9.488 | 11.14 | 13.28 | 18.47 |
| 5 | 9.236 | 11.07 | 12.83 | 15.09 | 20.52 |
| 6 | 10.64 | 12.59 | 14.45 | 16.81 | 22.46 |
| 7 | 12.02 | 14.07 | 16.01 | 18.48 | 24.32 |
| 8 | 13.36 | 15.51 | 17.53 | 20.09 | 26.12 |
| 9 | 14.68 | 16.92 | 19.02 | 21.67 | 27.88 |
| 10 | 15.99 | 18.31 | 20.48 | 23.21 | 29.59 |
| 11 | 17.28 | 19.68 | 21.92 | 24.72 | 31.26 |
| 12 | 18.55 | 21.03 | 23.34 | 26.22 | 32.91 |
| 13 | 19.81 | 22.36 | 24.74 | 27.69 | 34.53 |
| 14 | 21.06 | 23.68 | 26.12 | 29.14 | 36.12 |
| 15 | 22.31 | 25 | 27.49 | 30.58 | 37.7 |
| 16 | 23.54 | 26.3 | 28.85 | 32 | 39.25 |
| 17 | 24.77 | 27.59 | 30.19 | 33.41 | 40.79 |
| 18 | 25.99 | 28.87 | 31.53 | 34.81 | 42.31 |
| 19 | 27.2 | 30.14 | 32.85 | 36.19 | 43.82 |
| 20 | 28.41 | 31.41 | 34.17 | 37.57 | 45.31 |
| 21 | 29.62 | 32.67 | 35.48 | 38.93 | 46.8 |
| 22 | 30.81 | 33.92 | 36.78 | 40.29 | 48.27 |
| 23 | 32.01 | 35.17 | 38.08 | 41.64 | 49.73 |
| 24 | 33.2 | 36.42 | 39.36 | 42.98 | 51.18 |
| 25 | 34.38 | 37.65 | 40.65 | 44.31 | 52.62 |
| 26 | 35.56 | 38.89 | 41.92 | 45.64 | 54.05 |
| 27 | 36.74 | 40.11 | 43.19 | 46.96 | 55.48 |
| 28 | 37.92 | 41.34 | 44.46 | 48.28 | 56.89 |
| 29 | 39.09 | 42.56 | 45.72 | 49.59 | 58.3 |
| 30 | 40.26 | 43.77 | 46.98 | 50.89 | 59.7 |
Privacy: how it works
- The test is calculated by code in your own browser tab. Your counts are not sent to Ulkaa or any other server.
- There is no account and nothing is stored once you close the tab.
Tips
- Enter counts, not percentages. Percentages change the sample size and so the statistic.
- For a 2 by 2 table the test of independence with no continuity correction can be a little too liberal. Compare with Fisher’s exact test when counts are small.
- Look at the contributions to see which cells drive the result, instead of stopping at the p-value.
- Rows and columns of a table must each contain at least one non-zero count.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your counts are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your counts are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I use a chi-square table?
Find the row for your degrees of freedom and the column for your significance level. If your statistic is larger than that value, reject the null hypothesis.
Why are all the values right-tailed?
Chi-square tests measure how far the data are from the null hypothesis, so only large values count as evidence against it.
More Chi-Square Calculator pages
- Chi-Square CalculatorRun a chi-square goodness-of-fit test or a test of independence on a contingency table, with expected counts and Cramér’s V.
- Chi-Square Goodness of Fit CalculatorType the observed counts and see whether they match what you expected.
- Chi-Square Test of Independence CalculatorEnter a table of counts and see whether the two variables are related.