Z-Score Calculator
Calculate a z-score (how many standard deviations a value is from the mean) and its percentile.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter a value, mean, and standard deviation to find the z-score and percentile.
Your result
1.5
Z-score
Percentile93.319
AI explanation
Formula
Z = (value − mean) ÷ standard deviation; percentile from the standard normal distributionWorked example
Value 85, mean 70, standard deviation 10
| Field | Value |
|---|---|
| Value | 85 |
| Mean | 70 |
| Standard deviation | 10 |
| Z-score | 1.5 |
| Percentile | 93.32 |
Assumptions
- Assumes the data is normally distributed — the percentile uses the standard normal cumulative distribution function, which is only accurate for approximately normal data.
- The percentile uses a rational approximation of the normal CDF (Abramowitz-Stegun), accurate to within about 0.00001%.
Frequently asked questions
What does a z-score of 0 mean?
A z-score of 0 means the value equals the mean exactly.
What does the percentile tell me?
It's the percentage of a normally distributed population expected to fall below your value — a z-score of 1.5 corresponds to roughly the 93rd percentile.
Does this work for non-normally distributed data?
The z-score itself (how many standard deviations from the mean) is always valid, but the percentile figure specifically assumes a normal distribution and may not be accurate for skewed or non-normal data.