Z-score and normal distribution calculator
Calculate the z-score of a value, the cumulative probability and the percentile on the normal distribution, or go the other way, with a bell curve chart and the shaded area.
How to useZ-score, percentile and probability on the normal curve
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Z-score and normal distribution calculator: what it is for
Enter the mean and standard deviation and calculate from a value, a z-score, a percentile or a range between two values. The tool shows the z-score, the matching value, the probability below and above, the two-tailed probability and draws the normal curve with the shaded area.
The calculations run in your browser; nothing you type is sent to servers.
How to use
- Enter the mean and standard deviation.
- Choose the type of calculation and type the value.
- See the probabilities and the chart.
When to use it
- Compare scores from different tests.
- Interpret standardized tests.
- Study the normal distribution.
Frequently asked questions
What is a z-score?
It is how many standard deviations a value is above or below the mean: z = (x − mean) / standard deviation. A z of 1.5 means a value 1.5 deviations above the mean.
How do I turn z into a percentile?
With the normal cumulative distribution function. A z of 0 is the 50th percentile, z = 1 the 84.1th and z = 1.96 the 97.5th. The tool does this calculation and the reverse.
What is it used for?
To compare scores from different tests, read children's growth charts, work out the chance of a value going past a limit and understand standardized test results.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.