This z-score calculator standardizes a raw value against a mean and standard deviation, and shows the matching percentile.
Statistics
Z-score Calculator
Convert an observation into standard deviations from the mean.
Calculator
About this calculator
Formula notes
z = (x − μ) / σ. Positive z means above average; the percentile comes from the standard normal table.
Worked examples
- Example: x one SD above the mean gives z = 1 and percentile ≈ 84.13.
- An observation of 72 in a distribution with mean 60 and standard deviation 8 has z = (72 - 60) / 8 = 1.5.
How to use it
- Enter the raw value, mean, and standard deviation.
- Read the z-score for standardized comparison.
- Read the percentile for the normal-model share below it.
Frequently asked questions
What does z = −2 mean?
The value sits two standard deviations below the mean — roughly the 2.3rd percentile in a normal model.
Does z assume normality?
The z-score itself is just a rescaling; the percentile readout assumes a normal distribution.
Limits and interpretation
- A z-score is undefined when standard deviation is zero and only has meaning relative to the stated reference distribution.
- Converting z to a normal percentile additionally assumes a normal model; standardization alone does not make data normal.