Z-Score Calculator

Express a value's distance from the mean in standard-deviation units. Enter your own values below to see z-score and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

Let’s work it out.

Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

Z = (observed value − population mean) ÷ population standard deviation.

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What is Z-Score Calculator?

Z-Score Calculator helps you express a value's distance from the mean in standard-deviation units.

The main result is z-score. The formula, example and assumptions below explain how to interpret it.

How to use Z-Score Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather observed value, population mean and population standard deviation. Use values from the same situation or reporting period.
  2. Replace the example observed value with your own value, then complete the other fields. Check the displayed units.
  3. Select Calculate and read z-score. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter observed value, at least -1000000000000. Decimals are accepted.
  • Enter population mean, at least -1000000000000. Decimals are accepted.
  • Enter population standard deviation, at least 0.000001. Decimals are accepted.

Z-Score Calculator: a worked example

With the inputs below, the result is 1.5 (z-score). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
Observed value85
Population mean70
Population standard deviation10
Z-score1.5

Understanding the Z-Score result

The main output is z-score. It applies to the inputs and operation you selected.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

Z-Score Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Z-Score Calculator FAQs

What does Z-Score Calculator calculate?

Z-Score Calculator helps you express a value's distance from the mean in standard-deviation units. Its main output is z-score.

What inputs do I need for Z-Score Calculator?

You need observed value, population mean and population standard deviation. Use the field labels and units to match your figures to the formula.

Which formula does Z-Score Calculator use?

Z = (observed value − population mean) ÷ population standard deviation.

What is a worked example for Z-Score Calculator?

Example inputs: Observed value: 85; Population mean: 70; Population standard deviation: 10. The result is 1.5 (z-score).

How should I enter observed value?

Enter observed value, at least -1000000000000. Decimals are accepted.

How do I choose population mean?

Enter population mean, at least -1000000000000. Decimals are accepted. The example uses 70; replace it if your circumstances differ.

How should I read z-score?

The main output is z-score. It applies to the inputs and operation you selected.

Why might my Z-Score Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Z-Score Calculator?

Yes. Note your first z-score, change observed value or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Z-Score Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.