Convert a value to a standard score and find its percentile in a normal distribution.
How z-score is worked out
A z-score says how many standard deviations a value is from the mean. Enter the value, mean and standard deviation and this calculator returns the z-score and the percentile it corresponds to.
It’s a staple of statistics and standardized testing.
Step by step
- Enter the value.
- Enter the mean and standard deviation.
- Read the z-score and percentile.
The calculation
z = (x − mean) ÷ standard deviation
The default scenario, worked through
On the values this calculator opens with, the z-score is 1.5. Underneath, Percentile comes out at 93.3th and Area to left at 0.9332. Change any field and every figure updates as you type.
Common questions
What is a z-score?
How far a value sits from the mean, measured in standard deviations. A z of +2 is two standard deviations above average.
What does the percentile mean?
The share of a normal distribution below your value — a z-score of 0 is the 50th percentile.
When are z-scores used?
Comparing scores across different scales, spotting outliers, and standardized test reporting.