Math
Z-Score Calculator
Calculate z-scores, find the original value, mean, or standard deviation. Includes percentile estimate for normal distributions.
Enter values above (standard deviation must be positive)
Advertisement
Z-Score Formula
Z = (x − μ) / σ
Where x is the data point, μ is the population mean, and σ is the standard deviation.
Rearranging: x = Z × σ + μ, μ = x − Z × σ, σ = (x − μ) / Z
How to Use This Calculator
Choose which value you want to find — z-score, data value (x), mean (μ), or standard deviation (σ) — then enter the other three known values.
When calculating a z-score, the calculator also shows the approximate percentile using a normal distribution approximation.
Frequently asked questions
What is a z-score?
A z-score (or standard score) measures how many standard deviations a data point is from the mean of its distribution. A z-score of 0 means the value equals the mean.
What does a z-score of 2 mean?
A z-score of 2 means the data point is two standard deviations above the mean. In a normal distribution, about 97.7% of values fall below this point.
What does a negative z-score mean?
A negative z-score means the value is below the mean. For example, a z-score of −1.5 means the value is 1.5 standard deviations below the mean.
How is a z-score related to percentile?
In a normal distribution, z-scores map directly to percentiles. A z-score of 0 corresponds to the 50th percentile, a z-score of 1 to approximately the 84th percentile, and a z-score of −1 to approximately the 16th percentile.
When should you use z-scores?
Z-scores are useful when comparing values from different scales or distributions, identifying outliers, standardising data before machine learning, or calculating probabilities from a normal distribution.