About Z-Score Calculator
A z-score states how many standard deviations a value lies above or below the mean: z = (x − μ) ÷ σ. The calculator then converts z to a percentile with a polynomial approximation of the standard normal cumulative distribution (Abramowitz and Stegun, accurate to about seven decimal places). The percentile is meaningful only if the data is roughly normally distributed. The standard deviation must be greater than zero.
How to use Z-Score Calculator
- Fill in "Value", "Mean" and "Standard deviation".
- The result appears below and updates as you type.
- Copy the result with the copy button, or download it as a file where that is offered.
Questions about Z-Score Calculator
What does a z-score of 1.5 mean?
The value is 1.5 standard deviations above the mean. On a normal distribution about 93.3% of values fall below it and about 6.7% fall above it.
Can a z-score be negative?
Yes. A negative z-score means the value is below the mean. A z-score of −1 sits one standard deviation below the mean, at roughly the 16th percentile of a normal distribution.
Runs in your browser. Page last updated .