BYTETOOLS

P-Value Calculator

Turn a z, t, chi-square or F test statistic into left-tail, right-tail and two-tailed p-values, with the critical value and a reject or fail-to-reject verdict.

0.975002
Left-tail p
0.024998
Right-tail p
0.049996
Two-tailed p

Decision

Two-tailed: Reject the null hypothesis (p ≤ α = 0.05)

Right-tailed: Reject the null hypothesis (p ≤ α = 0.05)

1.64485
One-tailed critical value (α = 0.05)
1.95996
Two-tailed critical value (α = 0.05)

Standard normal: P(Z ≤ z) = ½·erfc(−z/√2)

What is the P-Value Calculator?

The ByteTools P-Value Calculator converts a test statistic into a p-value for the four distributions that cover almost every introductory and intermediate hypothesis test: the standard normal (z), Student's t, chi-square and F.

  • Four distributions on one page: z, t, chi-square and F
  • Left-tail, right-tail and two-tailed p-values side by side
  • One- and two-tailed critical values at your chosen alpha
  • Accurate deep into the tails, not capped at a table's last row
  • Plain-English reject / fail-to-reject verdict
  • Runs entirely in your browser — nothing is uploaded

How to use the P-Value Calculator

  1. 1

    Choose the test distribution: z, t, chi-square or F.

  2. 2

    Type the test statistic you obtained.

  3. 3

    Enter the degrees of freedom (numerator and denominator for F).

  4. 4

    Pick your significance level alpha from the dropdown.

  5. 5

    Read the left, right and two-tailed p-values, the critical values and the verdict, then click Copy results.

About the P-Value Calculator

The ByteTools P-Value Calculator converts a test statistic into a p-value for the four distributions that cover almost every introductory and intermediate hypothesis test: the standard normal (z), Student's t, chi-square and F. Pick the distribution, type the statistic, add the degrees of freedom where they apply, and the left tail, right tail and two-tailed probability appear together.

It is built for students checking homework, researchers writing up a result and anyone who has a statistic from software but no p-value next to it. Alongside the probabilities you get the one- and two-tailed critical values at your chosen alpha and a plain-English verdict, so you can see both the p-value route and the critical-value route to the same decision.

Everything is computed in your browser with hand-written implementations of the error function, the regularized incomplete gamma and the regularized incomplete beta — the same special functions statistical packages use. No data is uploaded, nothing is stored, and the page works offline.

Frequently asked questions

What does a p-value actually mean?

A p-value is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. It is not the probability that the null hypothesis is true. A small p-value means your data would be surprising under the null, which is why it counts as evidence against it.

Should I use a one-tailed or two-tailed p-value?

Use a two-tailed p-value when your hypothesis is simply that there is a difference in either direction, which covers most situations. Use a one-tailed value only when you decided in advance that a difference in one specific direction is the only one of interest. Switching after seeing the data inflates your false positive rate.

Is a p-value of exactly 0.05 significant?

By the usual convention p is compared with alpha and 0.05 is not less than 0.05, so it sits right on the boundary. This calculator reports reject when p is less than or equal to alpha, and shows the exact p-value to six decimals so you can see how close the call really is.

Why do chi-square and F tests only show a right tail?

Chi-square and F statistics measure how far the data are from the null in one direction only, so larger values always mean more evidence against the null. The tool still shows a two-tailed figure using the standard 2 × min(left, right) convention, which is useful for variance-ratio tests.

Why does this p-value differ slightly from my textbook table?

Printed tables round critical values to three or four decimals, so working backwards from them gives a rounded p-value. This calculator evaluates the distribution functions directly to full double precision, which is why it matches statistical software rather than the table.

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