About this calculator
The calculator also gives the area under the normal curve to the left and right, which is the percentile if the data are normally distributed.
How to use it
- Choose whether to find the z-score or the value.
- Enter the value or z-score, the mean and the standard deviation.
- Read the result and the percentile.
The formula
z = (x − μ) ÷ σ; x = μ + zσ
- x
- value
- μ
- mean
- σ
- standard deviation
Worked example
A score of 78 where the mean is 65 and σ is 8
- z = (78 − 65) ÷ 8 = 1.625.
- The area to the left is 94.79%, so the score is at about the 95th percentile.
What the result means
z = 0 is the mean. Beyond ±2 is unusual (about 5% of values), and beyond ±3 is rare (about 0.3%).
Assumptions
- The percentile uses the normal distribution.
Limitations
- For skewed data the percentile from the normal curve can be off; use the percentile calculator on the raw data instead.
Frequently asked questions
What does a negative z-score mean?
The value is below the mean.
How do I compare scores from two exams?
Convert each to a z-score with its own exam’s mean and standard deviation; the higher z is the better relative result.
What z-score is the 95th percentile?
About 1.645.
Last reviewed on 6 October 2026. Found a mistake? Tell us.