Calculating the Coefficient of Variation
Divide the standard deviation by the mean and multiply by 100 to express the coefficient of variation as a percentage. Enter raw data—or a known mean and SD—to see the complete calculation.
Written and checked by TheToolNet Editorial Team · Last reviewed: August 22, 2026 · How we check statistics tools
The correct statistical term is coefficient of variation. “Coefficient of variance” is a common wording error; variance and standard deviation are not interchangeable.
Coefficient of variation calculator
Use raw observations or summary statistics. CV is most meaningful for ratio-scale measurements with a meaningful zero and a positive mean.
How to calculate coefficient of variation
- Calculate the arithmetic mean of the observations.
- Calculate sample standard deviation if the data are sampled from a larger population, or population SD if the values are the complete population.
- Divide the standard deviation by the mean.
- Multiply by 100 to report CV as a percentage.
A CV of 12% says the standard deviation is 12% of the mean. It does not say that 12% of observations are unusual or outside a limit.
Coefficient of variation worked example
For sample values 10, 12, 11, 9, and 8, the mean is 10 and sample SD is approximately 1.5811. Therefore CV = 1.5811 ÷ 10 × 100 ≈ 15.811%. The calculator also reconstructs the SD from mean × CV ratio as a check.
When coefficient of variation is meaningful
CV is intended for ratio-scale data: continuous measurements with a meaningful zero, such as length, mass, duration, or Kelvin temperature. It is useful when comparing relative variability across data sets with different units or substantially different means.
Use caution near zero. A zero mean makes CV undefined, and a mean close to zero can make it unstable. Interval scales such as Celsius or Fahrenheit do not have a meaningful absolute zero, so their CVs change when the same temperatures are converted between scales.
Coefficient of variation versus RSD, variance, and SD
| Measure | Formula | Meaning |
|---|---|---|
| Coefficient of variation | SD ÷ mean | Signed relative spread, commonly shown as a percentage. |
| Relative standard deviation | SD ÷ |mean| × 100% | Magnitude of relative spread as a non-negative percentage. |
| Standard deviation | √variance | Absolute spread in the original unit. |
| Variance | Average squared deviation | Absolute spread in squared units. |
For data with a positive mean, percentage CV and RSD have the same numerical value. Use our relative standard deviation in Excel guide for the spreadsheet formula.
Frequently asked questions
Is it coefficient of variance or coefficient of variation?
Coefficient of variation is the accepted statistical term. It uses standard deviation, not variance, in the numerator.
Is a lower CV always better?
No universal cutoff applies. A lower CV means less relative spread, but whether that is desirable depends on the measurement and decision.
Can CV be negative?
The signed formula can return a negative value when the mean is negative, but ordinary CV interpretation is generally not meaningful in that situation.
What happens when the mean is zero?
CV is undefined because its formula divides by the mean.
Related tools and authoritative reference
Compare two planned and actual values with the variance percentage calculator. For frequency tables, use the grouped-data standard deviation calculator.