Z-Score Calculator
Convert a value to a z-score (standard score) and find its percentile in a normal distribution.
About the Z-Score Calculator
A z-score says how many standard deviations a value is from the mean. It lets you compare scores on different scales, such as a maths test and an English test, and find what share of a normal population falls below a value.
The formula
z = (x − μ) ÷ σ
Common z-scores
| z | Share below |
|---|---|
| -3 | 0.135% |
| -2 | 2.275% |
| -1.645 | 4.998% |
| -1 | 15.866% |
| 0 | 50% |
| 1 | 84.134% |
| 1.645 | 95.002% |
| 1.96 | 97.5% |
| 2 | 97.725% |
| 2.576 | 99.5% |
| 3 | 99.865% |
Worked example
Example: z-score = 1.545455
- Inputs: Value (x): 94; Mean (μ): 77; Standard deviation (σ): 11.
- Formula: z = (x − μ) ÷ σ
- Subtract the mean and divide by the standard deviation z = (94 − 77) ÷ 11 = 1.545455
- Result: z-score = 1.545455
- Percentile: 93.8882th
- P(X < x): 0.93888182
- P(X > x): 0.06111818
Questions people ask
Is a z-score of 2 unusual?
Fairly: only about 2.3% of a normal population is that far above the mean.
Can I use it for any data?
The z-score itself, yes. Turning it into a percentile assumes the data are roughly normal.