P Value Calculator
Enter a z test statistic and tail choice to get its p-value from the standard normal distribution — plus a plain-English verdict at your significance level.
Example: with Test statistic (z) 1.96 · Test type Two-tailed · Significance level (Ξ±) 0.05 → P-value: 0.0500.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outHow to find the p-value from a test statistic
A p-value is the probability of seeing a test statistic at least as extreme as yours if the null hypothesis were true. For a z statistic it comes straight from the standard normal CDF Φ(z): two-tailed p = 2 × (1 − Φ(|z|)), right-tailed p = 1 − Φ(z), left-tailed p = Φ(z). Example: z = 1.96 two-tailed gives 2 × (1 − 0.9750) = 0.05; z = 2.00 right-tailed gives 1 − 0.9772 = 0.0228.
Pick the tail before you look at the data: two-tailed when any difference matters (the default in most journals), one-tailed only when the hypothesis was directional from the start. Then compare p to α: p ≤ 0.05 is conventionally “statistically significant,” but report the exact value — p = 0.049 and p = 0.001 are very different strengths of evidence.
How itβs calculated
Φ(z) is computed with the Abramowitz & Stegun 7.1.26 rational approximation of erf (maximum absolute error about 1.5 × 10⁻⁷, far below the 4 decimals shown). Two-tailed p = 2(1 − Φ(|z|)); right-tailed p = 1 − Φ(z); left-tailed p = Φ(z). Values below 0.0001 display as < 0.0001.
Results update as you type and are estimates, not professional advice β verify important decisions with a qualified professional.
Common mistakes
- Choosing one-tailed after seeing the data to halve the p-value β decide the tail in advance.
- Treating p as the probability the null is true β it's the probability of data this extreme given the null.
- Using a z p-value for small samples with unknown population SD β that calls for a t distribution with n β 1 degrees of freedom.
Frequently asked questions
How do I find the p value from a z test statistic?
Look up Φ(z) and take 2 × (1 − Φ(|z|)) for two-tailed, 1 − Φ(z) for right-tailed, or Φ(z) for left-tailed. This page does the lookup for you.
What is the p-value for z = 1.96?
Two-tailed, p ≈ 0.05 — exactly at the conventional cutoff. One-tailed it’s 0.025.
Is p = 0.05 significant?
By convention, p ≤ 0.05 is called statistically significant at the 5% level. It’s a threshold, not proof — always report the exact p-value too.
Can a p-value be zero?
No. It can be extremely small (this calculator reports anything below 0.0001 as < 0.0001), but some probability of extreme data always remains.
Should I use a one-tailed or two-tailed test?
Two-tailed unless you specified a direction before collecting data. For the same z, a one-tailed p is half the two-tailed p.