This z-score calculator tells you how many standard deviations a value sits above or below the mean, and converts that z-score to a percentile and to probabilities under the normal curve. Enter a value, mean and standard deviation — or enter a z-score directly to convert it.
What Is a Z-Score?
A z-score (or standard score) measures where a value sits inside a distribution, in standard-deviation units. A z-score of 0 is exactly the mean; +1 is one standard deviation above it; −2 is two below. Because z-scores strip away the original units, they let you compare things measured on completely different scales — a test score with a class mean of 70 and another with a mean of 200, for instance. This tool is part of our Statistics Calculators collection.
The Z-Score Formula
z = (x − μ) ÷ σ — value minus mean, divided by standard deviation.
Example (verified): a score of 85 where the mean is 70 and the standard deviation is 10 → z = (85 − 70) ÷ 10 = 1.50. That is the 93.32nd percentile: P(X < x) = 93.32%, and only 6.68% of scores are higher. If you do not know your data’s standard deviation yet, compute it with the Standard Deviation Calculator first.
Z-Score to Percentile (Common Values)
| Z-score | Percentile | Z-score | Percentile |
|---|---|---|---|
| −2.0 | 2.28 | +0.5 | 69.15 |
| −1.5 | 6.68 | +1.0 | 84.13 |
| −1.0 | 15.87 | +1.5 | 93.32 |
| −0.5 | 30.85 | +2.0 | 97.72 |
| 0 | 50.00 | +3.0 | 99.87 |
The table is symmetric: the percentile for −z is 100 minus the percentile for +z. Enter any z-score in the “directly” box above for values not in the table.
Where Z-Scores Are Used
- Exams and grading: comparing performance across different tests and classes.
- Growth charts: child height/weight z-scores are the basis of WHO and CDC charts.
- Finance: the Altman z-score gauges company bankruptcy risk (a different formula sharing the name).
- Quality control: flagging measurements outside ±3σ for investigation.
- Research: standardizing variables before comparison or modeling.
For event-style probabilities (dice, coins, cards) use the Probability Calculator; for centers of data sets, the Mean Median Mode Calculator.
Related Tools
- Standard Deviation Calculator — get σ for your data
- Probability Calculator — event probabilities
- Mean Median Mode Calculator
Frequently Asked Questions
What does a z-score of 0 mean?
The value equals the mean exactly — the 50th percentile.
Can a z-score be negative?
Yes. Negative means below the mean; positive means above it. The size shows the distance in standard deviations.
What z-score is the 95th percentile?
About +1.645. The 99th percentile is about +2.326, and the 90th is +1.282.
Do percentiles from z-scores assume a normal distribution?
Yes — the percentile conversion uses the normal (bell) curve. The z-score itself can be computed for any data, but percentile interpretation is exact only for approximately normal data.
How do I find a z-score in Excel?
=(x − AVERAGE(range)) / STDEV(range), or =STANDARDIZE(x, mean, sd). The percentile is =NORMSDIST(z).
Is this z-score calculator free?
Yes — free, instant, no sign-up.