Coefficient of Variation Calculator
Compare relative variability by dividing a data set standard deviation by its mean. The calculator uses the population standard deviation convention.
How to use this calculator
- Enter at least two numeric observations and check that their mean is positive.
- Review the worked example for coefficient of variation calculator and compare the inputs with your own units.
- Change one assumption at a time and recalculate if you need a second scenario.
Population coefficient of variation
CV = population standard deviation ÷ arithmetic mean × 100%.
- The population variance divides squared deviations by the number of observations. Sample CV uses a different standard deviation when the data represent a sample.
- The result is calculated from the values entered; the page does not independently verify assumptions, data quality or real-world suitability.
Worked examples
A small three-value set
For observations 8, 10 and 12, the mean is 10 and population standard deviation is about 1.633.
1.633 ÷ 10 × 100 ≈ 16.33%.
Coefficient of variation is approximately 16.33%.
Understanding the result
CV expresses spread relative to the mean, which can help compare data sets with different scales.
CV is not generally meaningful for means near zero, negative means or interval scales where zero is arbitrary.
Important notes
State whether population or sample variation is used when publishing a result.
Displayed figures are rounded for readability. Preserve more precision during intermediate calculations and verify the labels and units before using the estimate.
Frequently asked questions
What does the Coefficient of Variation Calculator show?
CV expresses spread relative to the mean, which can help compare data sets with different scales.
What assumptions should I check?
State whether population or sample variation is used when publishing a result.
Does this replace expert or authoritative guidance?
CV is not generally meaningful for means near zero, negative means or interval scales where zero is arbitrary.
Related calculators
- Standard Deviation Calculator — Calculate population or sample standard deviation, variance, mean, sum, and count.
- Mean Absolute Deviation Calculator — Measure the average absolute distance of data values from their arithmetic mean.
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
- Correlation Coefficient Calculator — Calculate the Pearson correlation coefficient for paired numeric observations and see the direction and strength of their linear association.
- Z-Score Calculator — Calculate the z-score of a value using its mean and standard deviation.
- Circle Calculator — Calculate circle area, circumference, and diameter from radius.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.