Z-Score & P-Value Calculator

About this calculator

Knowing a raw value, like a test score of 85, tells you very little on its own; what matters is how unusual it is relative to the group it came from, and translating that into a percentile or p-value requires the standard normal distribution, which isn't something you look up quickly by hand. This calculator takes a value, a mean and a standard deviation and computes the z-score as z = (x − μ) ÷ σ, the number of standard deviations the value sits from the mean, then converts that z-score into a percentile and both one-tailed and two-tailed p-values using the standard normal cumulative distribution function. The one-tailed p-value covers the probability of a value at least this extreme in one direction; the two-tailed p-value doubles that to cover both directions, which is the more common choice absent a specific directional hypothesis. It assumes the underlying data is approximately normally distributed, since z-scores and their associated percentiles only carry that interpretation under normality. That saves looking up a z-table or approximating the normal CDF by hand.

Frequently asked questions