Z-Score Calculator
Enter a value, mean, and standard deviation to calculate the z-score and see where it falls on the normal distribution.
Enter Your Values
Results
Z-Score
1.0000
Percentile
84.13%
A value of 70 is higher than approximately 84.13% of values in a normal distribution with mean 60 and standard deviation 10.
Normal Distribution Curve
How the Z-Score Calculator Works
This calculator converts a raw value into a z-score, which tells you how many standard deviations that value is from the mean. It then converts the z-score into a percentile using the standard normal distribution, and plots the result on a bell curve.
Formula
Z = (x - mean) / standard deviation. The percentile is found from the area under the standard normal curve up to z, calculated with the normal cumulative distribution function.
Example
A test score of 82 with a class mean of 70 and standard deviation of 8 gives a z-score of 1.5, which is about the 93rd percentile, meaning the score is higher than roughly 93% of the class.
Limitations
This calculator assumes the underlying data is approximately normally distributed. For skewed data or small sample sizes, the percentile estimate from the normal curve may not accurately reflect the real distribution.
How to use the result responsibly
- Check that every input uses the unit and time period shown beside the field.
- Compare the result with the worked example and formula above.
- For financial, tax, health, or legal decisions, confirm current rules with a qualified professional or the relevant authority.
Frequently Asked Questions
What does a negative z-score mean?
A negative z-score means the value is below the mean. For example, a z-score of -1 is one standard deviation below average.
How do I turn a z-score into a percentile?
The percentile is the area under the standard normal curve to the left of the z-score, which this calculator computes automatically using the normal cumulative distribution function.
What is considered a high z-score?
Z-scores beyond +/-2 are relatively uncommon in a normal distribution (about the top or bottom 2.5%), and beyond +/-3 are rare (about 0.1%).
Related Tools
Editorially reviewed September 22, 2026. Read our calculation methodology and editorial policy.