TrueCalculator

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.

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