Z-Score Calculator
Convert a value to a z-score and find its percentile in a normal distribution.
What the Z-Score Calculator does
A z-score expresses how many standard deviations a value sits from the mean. It puts measurements on different scales onto a common footing, which is what makes it the basis of standardised testing, quality control and outlier detection.
Formula
z = (x − μ) ÷ σPercentile = Φ(z), the standard normal cumulative distribution
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Raw value (x) | number | Yes | — |
| Population mean (μ) | number | Yes | — |
| Standard deviation (σ) | number | Yes | Accepts more than 0. |
How to use it
- Enter Raw value (x), Population mean (μ) and Standard deviation (σ).
- Select Calculate.
Worked example
A test score of 85 where the mean is 70 and the standard deviation is 10.
- Value
- 85
- Mean
- 70
- Standard deviation
- 10
z = 1.5, placing the score at the 93.32nd percentile.
Frequently asked questions
What counts as an unusual z-score?
Beyond ±2 is conventionally unusual, covering about 5% of a normal distribution. Beyond ±3 is rare, at roughly 0.3%.
Can a z-score be negative?
Yes. A negative z-score simply means the value sits below the mean.