About P-Value from Chi-Square Calculator
This calculator finds the p-value of a chi-square statistic for any degrees of freedom, with the critical value and the shaded right tail. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Chi-square tests (goodness of fit, independence, variance) reject for large values, so the p-value is the area to the right of the statistic. The calculator opens on the right tail for that reason. The curve is skewed, and its shape changes a lot with the degrees of freedom: with 1 degree of freedom the density runs off to infinity at zero, and with large df it looks nearly normal.
If you have a table of observed counts rather than a statistic, the chi-square calculator on this site computes the statistic, the degrees of freedom and this p-value in one go.
How to use P-Value from Chi-Square Calculator
- Pick the distribution of your test statistic: z (normal), t, chi-square or F.
- Type the statistic. For t and chi-square add the degrees of freedom, and for F add the numerator and denominator degrees of freedom.
- Choose the alternative hypothesis: two-tailed (not equal), right-tailed (greater than) or left-tailed (less than).
- Choose a significance level, usually 0.05. The critical value and the shaded rejection region follow it.
- Read the p-value and the decision, then open the step-by-step working if you need to show it.
Features
- p-value from a z, t, chi-square or F statistic, left, right or two-tailed.
- Critical value or values for the chosen tail and significance level.
- Left and right tail areas shown separately, so you can check any one-sided claim.
- A bell curve with the rejection region shaded and your statistic marked, readable on a phone.
- Step-by-step KaTeX working and a copy button for the result.
- Non-integer degrees of freedom are accepted, for example the Welch value 17.776.
- A plain-English conclusion that says what the p-value means and what it does not.
Chi-square p-value
With Q the regularised upper incomplete gamma function:
p = P(χ² ≥ x) = Q(df / 2, x / 2)Worked examples
χ² = 11.07, df = 5, right-tailed gives p = 0.05001, critical value 11.07
χ² = 3.841, df = 1, right-tailed gives p = 0.05001, critical value 3.841
Privacy: how it works
- The p-values come from distribution functions that run in your browser tab. Nothing you type is sent to Ulkaa or anyone else.
- There is no account, and nothing is stored once you close the tab.
Tips
- Match the tail to the question you asked before you saw the data. Switching to a one-tailed test afterwards to get below 0.05 is not honest.
- Write the p-value with its test and degrees of freedom, for example t(10) = 2.23, p = 0.05, rather than only "significant".
- When software prints "p = 0.000", the true value is just very small. Report p < 0.001 instead.
- Degrees of freedom do not have to be whole numbers. Welch t-tests give fractional degrees of freedom, and you can type them as they are.
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 numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers 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.
Why is the chi-square p-value right-tailed?
Chi-square measures the distance between observed and expected counts, so only large values count as evidence against the null hypothesis. A small statistic simply means a good fit.
How do I find the degrees of freedom?
For a goodness-of-fit test it is the number of categories minus 1. For a test of independence it is (rows minus 1) times (columns minus 1).
More P-Value Calculator pages
- P-Value CalculatorTurn a z, t, chi-square or F statistic into a p-value, see the critical value, and watch the rejection region on the curve.
- P-Value from Z-Score CalculatorType a z-score and get the p-value, the critical value and the shaded normal curve.
- P-Value from T-Score CalculatorEnter a t statistic and its degrees of freedom to get the p-value and the critical t value.
- P-Value from F-Statistic CalculatorEnter an F statistic and both degrees of freedom to get the p-value and the critical F value.