Z-Score Calculator
Enter a value, the mean and the standard deviation to find the z-score, the percentile and the probability of a value above or below it on a normal curve.
Z-score formula
z = (x − μ) ÷ σ
A z-score tells you how many standard deviations a value is above or below the mean. Positive scores are above the mean and negative scores are below it.
Worked example
A test score of 85, where the mean is 70 and the standard deviation is 10, has z = (85 − 70) ÷ 10 = 1.5. On a normal curve about 93.32% of scores fall below it, so it is roughly the 93rd percentile.
Common z-scores
| Z-score | Percentile | Within ±z of the mean |
|---|---|---|
| 1.0 | 84.13% | 68.27% |
| 1.645 | 95.00% | 90.00% |
| 1.96 | 97.50% | 95.00% |
| 2.0 | 97.72% | 95.45% |
| 3.0 | 99.87% | 99.73% |
Percentiles assume the data are approximately normally distributed.
Frequently asked questions
What is a good z-score?
It depends on context. A z-score above 2 or below −2 is often considered unusual.
Can a z-score be negative?
Yes. A negative z-score means the value is below the mean.
How do I convert a z-score to a percentile?
Find the area to the left of z under the standard normal curve. The calculator does this automatically.
What is the difference between a z-score and a t-score?
A z-score uses a known population standard deviation; a t-score uses a sample standard deviation and a t distribution.
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