Z-Score Calculator
Convert a raw value into a z-score using the mean and standard deviation, and see its percentile on the standard normal curve.
- P(X < x)
- 0.9332
- P(X > x)
- 0.0668
A z-score of 1.5000 means the value is 1.5000 standard deviations above the mean.
Standard normal curve
z = 1.5000What is a z-score?
A z-score (or standard score) tells you how many standard deviations a value is from the mean. A positive z-score is above the mean; a negative one is below. Standardizing values this way lets you compare measurements from different distributions and read off probabilities from the standard normal distribution.
Z-score formula
The z-score subtracts the mean and divides by the standard deviation:
For a sample, use the sample mean (x̄) and sample standard deviation (s) in place of μ and σ.
Z-score to percentile
The percentile is the percentage of values that fall below your value. It equals the area to the left of the z-score under the standard normal curve, Φ(z). For example, a z-score of 0 is the 50th percentile, and a z-score of 1.96 is about the 97.5th percentile.
Z-score in Excel
Use =STANDARDIZE(x, mean, standard_dev) to get the z-score, and =NORM.S.DIST(z, TRUE) to convert it into a cumulative probability (percentile).
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. About 97.7% of values in a normal distribution fall below it, so it is roughly the 97.7th percentile.
Can a z-score be negative?
Yes. A negative z-score simply means the value is below the mean. A z-score of −1.5, for example, is 1.5 standard deviations below the mean.
How do I turn a z-score into a percentile?
Find the cumulative probability Φ(z) — the area to the left of the z-score under the standard normal curve — and multiply by 100. This calculator does it automatically.