About P-Value Calculator
This p-value calculator is free, needs no sign-up and runs in your browser, so the numbers you type are never uploaded. Choose the distribution your test statistic comes from (z, t, chi-square or F), type the statistic and the degrees of freedom, pick a left, right or two-tailed test, and read the p-value straight away.
Next to the p-value you get the critical value at your significance level, the area in each tail, and a decision: reject or fail to reject the null hypothesis. A bell curve draws the rejection region and marks your statistic on it, so you can see why the answer is what it is. A step-by-step panel writes the working in LaTeX, and a plain-English sentence explains the result.
Use it to check a textbook answer, to finish a hypothesis test when software printed only the statistic, or to look up the p-value for a published result. The calculator does not run the test itself. If you have raw data, the t-test and chi-square calculators on this site compute the statistic and call the same p-value engine.
How to use P-Value 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.
How the p-value is found
The p-value is the probability, when the null hypothesis is true, of a statistic at least as extreme as yours. For a right-tailed test it is the area to the right of the statistic, for a left-tailed test the area to the left. A two-tailed p-value doubles the smaller tail.
The critical value is the statistic that cuts off exactly the significance level in the tail. You reject the null hypothesis when the statistic is beyond it, which is the same as the p-value being below the significance level.
right-tailed p = P(T ≥ t) = 1 − F(t)
left-tailed p = P(T ≤ t) = F(t)
two-tailed p = 2 × min{ F(t), 1 − F(t) }
reject H0 when p < αWorked examples
z = 1.96, two-tailed gives p = 0.05, critical values ±1.96
The familiar 5% cut-off of the normal distribution.
t = 2.228, df = 10, two-tailed gives p = 0.05001, critical values ±2.228
This statistic sits exactly on the 5% critical value in the t table for 10 degrees of freedom.
χ² = 11.07, df = 5, right-tailed gives p = 0.05001, critical value 11.07
Matches the chi-square table entry for 5 degrees of freedom at 0.05.
F = 3.478, df1 = 4, df2 = 10, right-tailed gives p = 0.05, critical value 3.478
The 5% critical value from the F table for 4 and 10 degrees of freedom.
Standard normal critical values
| Significance level (α) | Two-tailed z | One-tailed z |
|---|---|---|
| 0.1 | 1.645 | 1.282 |
| 0.05 | 1.96 | 1.645 |
| 0.01 | 2.576 | 2.326 |
| 0.001 | 3.291 | 3.09 |
Good to know
Two-tailed p-values for chi-square and F
The z and t distributions are symmetric, so doubling the smaller tail is the natural two-tailed p-value. Chi-square and F are skewed. This calculator still doubles the smaller tail, which is the most common convention, but most chi-square and F tests (goodness of fit, independence, ANOVA) use only the right tail. Choose right-tailed for those.
What a p-value is not
A p-value is not the probability that the null hypothesis is true, and it is not the probability that your result happened by chance alone. A small p-value says the data would be surprising if the null hypothesis were true. It says nothing about how large or how important the effect is, so report an effect size and an interval as well.
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.
What is a p-value?
It is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. A small p-value means the data are hard to explain by the null hypothesis alone.
How do I get a p-value from a z score?
Look up the area in the tail. For a z of 1.96 the area to the right is 0.025, so the two-tailed p-value is 0.05. Choose z, type 1.96 and pick two-tailed to see it.
What is the difference between one-tailed and two-tailed?
A two-tailed test asks whether the parameter is different in either direction and splits the significance level across both tails. A one-tailed test asks about one direction only and puts the whole level in one tail, so its p-value is half the two-tailed one when the statistic lies in the expected direction.
When do I reject the null hypothesis?
Reject it when the p-value is below your significance level, usually 0.05. That is the same as the statistic falling in the shaded rejection region. If the p-value is at or above the level, you fail to reject. That is not proof that the null hypothesis is true.
Which tail should I use for chi-square and F?
Almost always the right tail. Large chi-square and F values mean a poor fit or large differences between groups, so the rejection region is on the right.
How accurate are the values?
They come from numerical evaluations of the incomplete gamma and beta functions and match standard statistical tables to the digits those tables print. Extremely small p-values are shown as p < 0.0001.
Can it run the test for me from raw data?
Not this page. It starts from a statistic you already have. The t-test calculator and the chi-square calculator on this site take raw data or summaries and compute the statistic and the p-value together.
Popular P-Value Calculator pages
- 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 Chi-Square CalculatorEnter a chi-square value and its degrees of freedom to get the right-tail p-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.