Z-Score Calculator
Enter a data value, population mean, and standard deviation to calculate the z-score and p-value.
Z-Score — Formula & Guide
Formula
z = (x − μ) / σ
Where x = data point, μ = mean, σ = standard deviation.
Frequently Asked Questions
What does a z-score of 2 mean?
A z-score of 2 means the value is 2 standard deviations above the mean, placing it at approximately the 97.7th percentile — better than ~97.7% of all values in a normal distribution.
How do I standardize data using z-scores?
Apply z = (x − mean) / SD to every data point. This converts data with any scale to a standard scale (mean 0, SD 1), allowing you to compare values from different distributions.
Interpretation
z = 0: value equals the mean • z = +1: one SD above the mean • z = −1: one SD below the mean.
For a standard normal: 68% of data falls within z = ±1, 95% within z = ±1.96.
