This p-value calculator converts a test statistic — z, t or chi-square — into its p-values: right-tailed, left-tailed and two-tailed, with the significance verdict at the conventional levels.
From Statistic to Probability
A p-value is a tail area: how much of the null distribution lies at least as far out as what you observed. Our Z-Score Calculator covers the normal special case (p from a z is its bread and butter); this page adds the t-distribution (extra width for small samples, governed by degrees of freedom) and chi-square (the independence/goodness-of-fit workhorse, right-tailed by construction). The Confidence Interval view is the same inference turned inside-out — an interval excluding the null ⟺ two-tailed p below the matching α. Part of our Statistics Calculators collection.
Worked Examples (Verified)
- z = 1.96: right-tail 0.0250, two-tailed 0.0500 — the most famous pair of numbers in statistics, the exact boundary of "significant at 0.05"
- t = 2.0, df = 10: two-tailed p ≈ 0.0734 — the same statistic that would pass as z fails as t, because estimating σ from 11 observations honestly fattens the tails
- χ² = 5.99, df = 2: right-tailed p = 0.0500 — the classic critical value from chi-square tables, reproduced
Reading P-Values Without Lying to Yourself
- p is not P(null is true), not P(result was chance), and not an effect size — a giant sample makes trivia "significant" (pair it with Cohen's d, on this hub, for magnitude).
- One-tailed tests double your sensitivity in one direction and blind you in the other; they need the direction chosen before data.
- 0.049 and 0.051 are evidentially near-identical; the bright line is a filing convention, not a law of nature — report the number, not just the verdict.
- Many tests inflate false positives (20 tests at α=0.05 expect one "hit" by luck) — corrections (Bonferroni, FDR) exist for exactly this.
Related Tools
- Z-Score Calculator — z to percentile and back
- Confidence Interval Calculator — the interval view of the same question
- Statistics Calculators — the full collection
Frequently Asked Questions
How do I get a p-value from a z-score?
Read the tail area beyond the z in the standard normal: z = 1.96 leaves 2.5% in the right tail, 5% two-tailed. Enter the statistic here and the calculator returns all three tails for whichever distribution your test uses.
What is the difference between one-tailed and two-tailed?
One-tailed tests ask "greater?" (or "less?") in a single pre-committed direction; two-tailed asks "different?" and splits the extremes across both tails — so two-tailed p is double the relevant one-tailed value (for symmetric distributions).
Why does t need degrees of freedom?
The t-distribution's shape depends on how much data estimated the standard deviation: df = n−1 for one-sample tests. Small df → fatter tails → larger p for the same statistic (t = 2.0: p = 0.046 as z-ish infinity, 0.073 at df 10). As df → ∞, t becomes z.
Is p < 0.05 proof my effect is real?
It is evidence against the null at a conventional strength — nothing more. Replication, effect size, study design and prior plausibility (Bayes, on this hub) complete the judgment. Fields from psychology to particle physics set their own bars (physics demands ~5σ, p ≈ 3×10⁻⁷).
Can a p-value be exactly 0?
No — tail areas approach zero asymptotically; software prints 0.0000 by rounding. Report as p < 0.0001. If this calculator shows a tiny exponential (like 2.4e-9), that's the honest form.
Is this p-value calculator free?
Yes — free, instant, no sign-up.