Z-Score Calculator
Find the z-score (standard score) of a value from the mean and standard deviation.
Z-Score Calculator
How many standard deviations a value is from the mean.
What a Z-Score Tells You
A raw number like “scored 80” does not mean much on its own - 80 could be excellent or poor depending on the test. A z-score fixes that by measuring a value in standard deviations from the mean: how far above or below average it sits, on a scale that works for any data set.
- A z-score of 0 means the value is exactly average.
- Positive means above average, negative means below.
- A z-score of 2 means “two standard deviations above the mean” - unusually high.
Because it is on a standard scale, a z-score lets you compare results from completely different tests. The number line by the calculator marks the mean and shows where your value lands.
Z-Score Formula
where x is the value, μ is the mean, and σ is the standard deviation.
How to Use It
- Enter the value, the mean, and the standard deviation.
- Read the z-score.
Worked Examples
| Value | Mean | SD | z-score |
|---|---|---|---|
| 80 | 65 | 10 | 1.5 |
| 50 | 65 | 10 | −1.5 |
| 65 | 65 | 10 | 0 |
| 90 | 70 | 8 | 2.5 |
FAQ
What is a z-score?
It is how far a value sits from the mean, measured in standard deviations. A z-score of 1.5 means the value is 1.5 standard deviations above the mean.
What does a negative z-score mean?
The value is below the mean. A z-score of 0 means it equals the mean.
How do I get the standard deviation?
Use the standard deviation calculator on your data set, then enter it here.