Z-Score Calculator

How to Calculate a Z-Score

A z-score tells you how many standard deviations a value is above or below the mean. It standardizes scores so you can compare different distributions.

The formula

z = (x − μ) ÷ σ

Where x = your value, μ = mean, σ = standard deviation.

Step-by-step

1. Enter the value you want to evaluate.
2. Enter the mean of the dataset.
3. Enter the standard deviation.
4. The z-score shows how unusual the value is.

Worked example

A test score of 75, class mean 70, standard deviation 5. z = (75 − 70) ÷ 5 = 1.0. This means the score is 1 standard deviation above average — better than ~84% of the class.

Interpreting z-scores

• z = 0: exactly at the mean
• z > 0: above the mean
• z < 0: below the mean
• |z| > 2: unusual (top or bottom ~2.3%)
• |z| > 3: very rare (top or bottom ~0.13%)