How this calculation works
A z-score expresses how far an observation lies from a supplied mean, measured in standard deviations. Positive scores are above the mean and negative scores below it. This standardisation helps compare relative positions on different scales, but does not by itself turn the score into a percentile.
z = (observed value − mean)/standard deviation, with a strictly positive standard deviation.
Worked example
This example uses illustrative inputs. Your current result is shown above.
For value 85, mean 70 and standard deviation 10, z = (85 − 70)/10 = 15/10 = 1.5. The observation is 1.5 standard deviations above the mean.
Assumptions and limits
- Value, mean and standard deviation must describe the same population or reference data and use the same unit.
- The standard deviation must be positive.
- The arithmetic does not require a normal distribution; interpreting z as a normal-tail probability does.
Questions people ask
Does a z-score of zero mean the original value is zero?
No. It means the original value equals the supplied mean. The original measurement can be any value.
Can I read a percentile directly from this result?
Only with a distributional model or reference distribution. A standard normal table is appropriate only if the normal model is justified.