When to use this calculator
Express a value’s distance from the mean in standard deviations. A z-score does not by itself imply a normal distribution or a specific probability.
Explore the descriptive statistics calculators for other questions in this topic. For a related calculation, use the At Least One Event Calculator: Calculate the probability of at least one success in independent identical trials.
PUTTING IT INTO PRACTICE
Z Score: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Observed value | 85 |
| Population mean | 70 |
| Population standard deviation | 10 |
| Result | 1.5 |
- Check the input labels and enter the example values above.
- Apply the relationship: z = (value − mean) ÷ standard deviation.
- The result is 1.5 , rounded for display.
How to interpret your result
A z-score does not by itself imply a normal distribution or a specific probability.
The mean, median, range and standard-deviation tools accept variable-length lists with their limits stated. Choose a sample or population denominator appropriately. A summary statistic does not validate the sampling process or explain causation.
Frequently asked questions
Should I use sample or population standard deviation?
Use population deviation for the complete population being described. Use the sample form when estimating variability from a sample under suitable assumptions.
How do I use the z score calculator?
Enter observed value, population mean, population standard deviation. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
z = (value − mean) ÷ standard deviation.
What should I check before using the result?
A z-score does not by itself imply a normal distribution or a specific probability.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: exploratory data analysis ↗. This is a topic reference, not an external review or endorsement of this tool.
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