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Z-Score Calculator

Calculate standard score.

Methodology, assumptions, and limitations

The z-score subtracts the population or sample mean from the observed value and divides by the standard deviation. The sign gives direction and the magnitude gives distance from the mean in standard-deviation units.

Assumptions
  • The standard deviation is positive and uses the same units as the value.
  • The mean and standard deviation describe the intended reference distribution.
  • Normal-distribution probabilities are used only when that model is appropriate.
Limitations
  • A z-score alone does not prove an observation is unusual or erroneous.
  • Skewed or heavy-tailed distributions may not support normal-probability interpretations.
  • Sample and population standard deviations answer different questions.

Sources and standards

Related calculators

Probability CalculatorMean Median Mode Calculator
Calculator
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Results
Z-Score
1.00
Analysis
Interpretation of the current calculator output

Calculation Summary

The current inputs have been processed for the z-score calculator. Review the results panel for the computed output and use the charts tab to compare the current values visually.

How to Read It

The main result shows the direct answer for your current inputs. Supporting sections below explain the method, example, and common questions so the result is easier to interpret.

How to Use

Step-by-step instructions
  1. 1Enter the value.
  2. 2Enter the mean.
  3. 3Enter the standard deviation.
  4. 4View the z-score.

Z-Score

Measures how many standard deviations a value is from the mean.
z = (x - μ) / σ

Variables:

xValue
μMean
σStandard deviation

Example

Test Score

Inputs:

Score:115
Mean:100
SD:15

Steps:

  1. 1.z = (115 - 100) / 15
  2. 2.z = 1.0
Result:
1.0

Frequently Asked Questions

What does a z-score mean?

z = 0 is average, z = 1 is one SD above average, z = -1 is one SD below.
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