Z-Score Calculator
Enter a value, the mean, and the standard deviation of its distribution to calculate the z-score — how many standard deviations that value sits from the mean — along with its approximate percentile under a normal distribution.
How the Z-Score formula works
The z-score formula:
z = (x − mean) / standard deviation
The percentile is then derived from the standard normal cumulative distribution function (CDF) evaluated at that z-score.
Step-by-step calculation
- Subtract the mean from your value.
- Divide the result by the standard deviation to get the z-score.
- Look up (or numerically approximate) the standard normal CDF at that z-score to get a percentile.
Worked example
A test score of 85, with a class mean of 75 and standard deviation of 10: z = (85 − 75) / 10 = 1.0. A z-score of 1.0 corresponds to roughly the 84th percentile under a normal distribution.
Frequently asked questions
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 is 1.5 standard deviations below average, corresponding to a low percentile.
Does this only work for normally distributed data?
The z-score itself can be calculated for any data set, but converting it to a percentile using the normal distribution assumes the underlying data is approximately normally distributed (bell-curve shaped) — for heavily skewed data, that percentile estimate becomes less accurate.