Z-Score Calculator
By Santaji GadepatilinUpdated October 27, 2026
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Type in any field to change it. Press × on a value to calculate that field instead.
Percentile (area to the left) (%) vs Value (x) — other inputs held at your current values.
How to use this calculator
Enter the value, the mean and the standard deviation. The z-score and percentile appear instantly. To find the value at a given percentile, press × on Value and type the percentile.
Formula
z = (x − μ) ÷ σ
Worked example
An exam score of 85 when the class mean is 70 and SD is 10:
- z = (85 − 70) ÷ 10 = 1.5
- Percentile = 93.3% — better than about 93% of the class
Common z-scores
| z | Percentile |
|---|---|
| −2 | 2.3% |
| −1 | 15.9% |
| 0 | 50% |
| 1 | 84.1% |
| 1.645 | 95% |
| 1.96 | 97.5% |
| 2 | 97.7% |
Frequently asked questions
What is a z-score?
How many standard deviations a value is above or below the mean. z = 0 is exactly average; z = 2 is two SDs above.
How do I find a percentile from a z-score?
Use the normal distribution — the calculator gives the share of values below x, assuming the data is normally distributed.
What z-score is unusual?
Values beyond about ±2 occur roughly 5% of the time; beyond ±3, about 0.3% of the time.