Z-Score Calculator
A z-score places any value on the normal curve: how many standard deviations it sits from the mean, and what share of the population falls below, above or between. Enter a score, a z or a percentile and every related number updates instantly. Everything runs in your browser.
IQ example preloaded: a score of 130 on a scale with mean 100 and SD 15.
97.7th percentile
How this is computed
pnorm() and qnorm().
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✓ Verified against R's pnorm() and qnorm() to 9 decimals
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The z-scores everyone ends up memorising
These critical values come up in every confidence interval and hypothesis test.
| z-score | Percentile | Where you meet it |
|---|---|---|
| 1.282 | 90% | 80% confidence intervals (10% in each tail) |
| 1.645 | 95% | 90% CIs and one-tailed tests at α = 0.05 |
| 1.960 | 97.5% | 95% CIs, the most famous number in statistics |
| 2.326 | 99% | 98% CIs and one-tailed tests at α = 0.01 |
| 2.576 | 99.5% | 99% confidence intervals |
Frequently asked questions
What is a z-score?
A z-score counts how many standard deviations a value sits above or below the mean. z = 2 means two standard deviations above average, z = -1.5 means one and a half below. It puts every measurement, heights, test scores, blood pressure, on one common scale.
How do I convert a z-score to a percentile?
The percentile is the area under the standard normal curve to the left of your z. For z = 2, that area is 0.977, so the value sits at the 97.7th percentile: higher than about 98 of every 100 observations.
What z-score is the 95th percentile?
z = 1.645. Two related values worth knowing: the 97.5th percentile is z = 1.960 (the boundary of a 95% confidence interval) and the 99th is z = 2.326.
Can a z-score be bigger than 3?
Yes, there is no upper limit. But values beyond |z| = 3 are rare under a normal distribution (fewer than 3 in 1,000), which is why they are often flagged as potential outliers.
Does this calculator match R?
Yes. Every probability and quantile is verified against R's pnorm() and qnorm() to nine decimal places, including deep tails past |z| = 4.