Z-Score Calculator
Find how many standard deviations a value sits above or below the mean, and its approximate percentile under a normal distribution.
Your results
Calculation breakdown
- Z-score
- z = (x − μ) / σ
Worked example
A student scores 88 in a test where the class mean is 75 and the standard deviation is 8. Their z-score is (88 − 75) / 8 = 1.625, meaning they scored 1.625 standard deviations above the mean.
Assumptions
- The percentile estimate assumes the underlying data is approximately normally distributed, which may not hold for small or skewed datasets.
- Enter the population mean and standard deviation if known, otherwise sample estimates are commonly used.
How this calculator works
Enter your value along with the mean and standard deviation of the group it belongs to. The calculator returns the z-score and an approximate percentile, assuming the data is roughly normally distributed.
Frequently asked questions
What does a z-score of 0 mean?
A z-score of 0 means the value is exactly equal to the mean of the dataset.
What's a 'good' z-score?
It depends on context — for test scores a positive z-score means above average, but there's no universal 'good' value outside the specific comparison being made.
Does this work for any dataset?
The percentile estimate is most accurate for data that is approximately normally distributed; skewed data will give a less reliable percentile.