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P-Value Calculator

Turn a z, t, or chi-square statistic into the probability figure your write-up actually needs.

Numbers in

Numbers out

P-value -
Significant at 0.05? -
Statistic -

This runs entirely client-side the instant you edit a field above.

How to read it

A p-value is the probability of seeing a result this extreme, or more extreme, if the null hypothesis were actually true. It is not the probability that the null hypothesis itself is true, and it says nothing about how large or meaningful an effect is, only how surprising the data would be under a specific assumption.

The usual cutoff: many fields treat p below 0.05 as "statistically significant," but that threshold is a convention, not a law of nature; some fields use 0.01, and pre-registered studies sometimes set their own.

What this calculator returns for a few benchmark inputs

These come straight from the same functions running the calculator above, so you can sanity-check your own result against them:

StatisticTwo-tailed p-value
z = 1.960.0500
z = 2.5760.0100
t = 2.0, df = 100.0734
t = 2.0, df = 300.0546
chi-square = 10, df = 100.4405

Notice t = 2.0 clears the 0.05 line only once df climbs toward 60; with few degrees of freedom, the t-distribution's fatter tails make the same statistic less impressive than it would be under a normal curve. See the t-test calculator to get a t-statistic from raw sample numbers, or the z-score calculator for the normal case.

Good to know

FAQs

Why does switching to Chi-square remove the two-tailed option?

Chi-square statistics are always zero or positive and the distribution itself is one-sided, so there's no lower tail to add. The tool locks to the upper tail automatically whenever you pick Chi-square.

I got p = 0.0000. Is that really zero?

No. Below 0.0001 the result switches to scientific notation instead of rounding to zero, so you'll see something like 3.217e-6 rather than a flat 0.0000. A true probability of exactly zero essentially never happens with continuous test statistics.

What's the real difference between one-tailed and two-tailed here?

Two-tailed asks how extreme your statistic is in either direction and doubles the one-sided area; one-tailed only counts the direction you specified in advance. Pick one-tailed only if you committed to that direction before seeing the data, not after.

Does a small p-value mean the effect is big or important?

No, and this is one of the most common misreadings of a p-value. It only measures how surprising your data would be if the null hypothesis were true; a huge sample can produce a tiny p-value for a practically trivial difference. Effect size is a separate calculation this tool doesn't attempt.

How accurate is the t and chi-square math here?

The t p-value comes from the regularized incomplete beta function and the chi-square p-value from the upper incomplete gamma function, both evaluated with the same continued-fraction and series methods used in standard numerical libraries. Results match dedicated statistical software to at least four decimal places for typical inputs.