Calculate z-scores, percentile ranks, probability areas, and raw scores from a mean and standard deviation with this free z-score calculator.
Z-score formula:
z = (x − μ) ÷ σ
Raw score formula:
x = μ + zσ
Percentile rank:
Use the standard normal distribution area to the left of z
Middle area:
Area between z and the mean or between two z-values
Z-scores standardize values so you can compare scores from different distributions. They are widely used in statistics, testing, finance, and research.
They help show whether a value is typical, unusually high, or unusually low compared to the mean.
Your result shows how far a value is from the mean in standard deviation units, or converts a z-score back into a raw value.
It also shows percentile rank, left-tail probability, right-tail probability, and the area between the mean and the z-score for easier interpretation.
A z-score tells you how many standard deviations a value is above or below the mean.
A negative z-score means the value is below the mean.
A z-score of 0 means the value is exactly equal to the mean.
Yes. A z-score can be converted into a percentile using the standard normal distribution.