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Z-Score Calculator

Express an observation as standard deviations above or below a known mean.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter observation, mean, standard deviation.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

z = (observation − mean) ÷ standard deviation. A positive score is above the mean and a negative score below it.

A WORKED EXAMPLE

An observation of 85 with mean 70 and standard deviation 10 has a z-score of 1.5.

What to keep in mind

Standard deviation must be positive. A z-score alone does not justify a normal-distribution probability or identify an outlier without context.

Common questions

What does z = 0 mean?

The observation equals the supplied mean.

Does z = 2 always imply a percentile?

No. Percentile interpretation requires a distributional model; this tool only standardizes the value.

Methodology maintained by ClarityKit. How these tools are built and checked.