P-Value Calculator
Compute two-tailed and one-tailed p-values from a z-score.
Input Data
Standardized test statistic.
Results
0.049996
0.975002
0.024998
At a glance:Two-tailed p = 2(1−Φ(|z|)); left-tail p = Φ(z); right-tail p = 1−Φ(z).
Formula
p(two-tailed) = 2 · (1 − Φ(|z|))
$$p = 2\left(1 - \Phi(|z|)\right)$$How to Use
- Enter the z-score z obtained from your test.
- Read the two-tailed p-value (most commonly used).
- For a one-tailed test, read the left-tail or right-tail p-value.
- If p < the significance level α (e.g. 0.05), reject the null hypothesis.
FAQ
What does a small p-value mean?
A small p-value means that, if the null hypothesis were true, observing such an extreme result would be very unlikely, so we tend to reject the null. The p-value is NOT the probability that the null hypothesis is true.
How do I choose two-tailed vs one-tailed?
Use two-tailed if you only care whether the result differs (greater or smaller); use one-tailed if you pre-specified a direction. The two-tailed p is about twice the one-tailed p.
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.