Statistics
Z-score calculator
Turn any value into a z-score — how many standard deviations it sits from the mean — and see the percentile that goes with it.
- Z-score
- 2
- Percentile (normal)
- 97.72%
The z-score is how many standard deviations the value sits from the mean. The percentile assumes a normal distribution — the share of values expected to fall below yours.
A common yardstick for “how unusual”
Raw numbers are hard to compare across different scales. A z-score fixes that by measuring everything in standard deviations from the mean, so a test score and a height can be judged on the same ruler. Positive means above average, negative below, and the size tells you how far out.
A worked example
An IQ of 130, where the mean is 100 and the standard deviation is 15, gives a z-score of (130 − 100) ÷ 15 = 2.0 — about the 97.7th percentile. Fewer than 3 in 100 people would score higher.
Related
Need the spread first? Use the standard deviation calculator, then build data fluency in the Statistics subject.
Frequently asked questions
- What is a z-score?
- A z-score is how many standard deviations a value sits above or below the mean. It’s calculated as (value − mean) ÷ standard deviation. A z of 0 is exactly average, +2 is two standard deviations above, and −1.5 is one and a half below.
- How do I turn a z-score into a percentile?
- For a normal distribution, the percentile is the share of values expected to fall below yours. A z of 2 corresponds to about the 97.7th percentile. This tool computes it for you using the standard normal distribution.
- What counts as an unusual z-score?
- Roughly 95% of values in a normal distribution fall within two standard deviations of the mean, so a z beyond ±2 is fairly unusual and beyond ±3 is rare. What’s “unusual” always depends on context, though.
- Does the percentile always apply?
- The percentile assumes the data is roughly normally distributed. For skewed data the z-score is still valid as a distance from the mean, but the percentile can be misleading.