Z-Score Calculator
Convert any value to a z-score and find its probability in a normal distribution.
Last updated: August 2026
The data point to standardize.
Z-score
1
Below
84.1%
Above
15.9%
Z = (x − μ) ÷ σ. Uses the standard normal distribution — assumes your data is roughly bell-shaped.
How it works
z = (x − μ) ÷ σ. Probability from the standard normal CDF (erf approximation).
Example: x=70, μ=60, σ=10 → z=1.0, 84.1% below.
Frequently Asked Questions
What is a z-score?
A z-score tells how many standard deviations a value is from the mean. A z of 2 means the value is two standard deviations above average.
How is the probability from a z-score found?
The calculator integrates the standard normal curve (via the error function) to find the area below the z-score, which equals the percentile.
When should I not use z-scores?
Z-score probabilities assume a normal (bell-shaped) distribution. For skewed or heavy-tailed data the probabilities can mislead.
What is a z-score table?
It lists the area under the normal curve for each z-value so you can look up probabilities by hand. This calculator computes the same numbers directly.