The coefficient of variation expresses the standard deviation as a percentage of the mean, which turns an absolute spread into a relative one. A deviation of 5 means something quite different around a mean of 10 than around a mean of 1000, and dividing by the mean is what makes those two situations comparable.
Because it is dimensionless it can compare a set of weights with a set of prices, or the volatility of two assets with very different price levels. It has one important limitation: it is only meaningful for ratio-scale data with a genuine zero and a positive mean. Applied to temperatures in Celsius, where zero is arbitrary, it produces nonsense.
Below the calculator sits the CV for a range of means and deviations table: 5 rows — 2 at one end, 50 at the other — which is usually faster than entering a value you have seen before. The page opens with standard deviation already set to 12, so there is a finished result on screen before anything is typed. The result is also read against 4 bands, from very consistent at the low end to highly variable at the high end, each with a note on what that range means in practice. Most visitors arrive here from, or leave for, Standard Error Calculator and Harmonic Mean Calculator.
The formula
σ- Standard deviation
μ- Mean of the data
CV- Coefficient of variation, as a percentage
How it works, step by step
- Enter the standard deviation of your data.
- Enter the mean.
- The gauge shows the coefficient of variation.
- The inverse ratio and one-deviation range appear below.
Worked examples
A deviation of 12 around a mean of 80
The coefficient is 12 ÷ 80 = 15%, so typical values fall between 68 and 92. That is moderate consistency for most measured processes.
Comparing two very different datasets
Weights averaging 70 kg with a deviation of 10 give a CV of 14.29%, while prices averaging £2,400 with a deviation of £300 give 12.50%. The prices are the more consistent set despite the far larger absolute spread.
Checking the 10 row
The reference table lists Deviation = 10, giving Mean 20: 50.00%, Mean 50: 20.00%, Mean 100: 10.00%, Mean 500: 2.00%. Entering that above should reproduce the same figures — if it does not, the input is being read differently to the way the table assumes.
How to read your score
Frequently asked questions
What counts as a good coefficient of variation?
It depends entirely on the field. Analytical chemistry might demand under 5%, while biological measurements routinely exceed 30%. Compare against the norm for your own domain.
Why must the mean be positive?
Because the coefficient is a ratio to the mean. Near zero it explodes, and for data with an arbitrary zero such as Celsius it has no meaning at all.
Is this the same as relative standard deviation?
Yes, the two terms are used interchangeably, with relative standard deviation more common in laboratory work.
How does it relate to the Sharpe ratio?
The Sharpe ratio is essentially the inverse idea applied to returns: excess return divided by deviation, so a high Sharpe corresponds to a low coefficient of variation.
What do the bands under the coefficient of variation mean?
They label the figure so it can be read without a reference point of your own: Very consistent from 0 to 10; Moderately consistent from 10 to 25; Variable from 25 to 50; Highly variable from 50 upwards. The band is a reading aid only — the number itself is exact, and a value sitting just over a boundary is not meaningfully different from one just under it.
What formula does the Coefficient of Variation Calculator use?
It computes CV = σ ÷ μ × 100%, where σ is standard deviation; μ is mean of the data; CV is coefficient of variation, as a percentage. The same expression is printed on the page above the inputs, so the result can be reproduced by hand or in a spreadsheet.
Coefficient of variation across scales
| Deviation | Mean 20 | Mean 50 | Mean 100 | Mean 500 |
|---|---|---|---|---|
| 2 | 10.00% | 4.00% | 2.00% | 0.40% |
| 5 | 25.00% | 10.00% | 5.00% | 1.00% |
| 10 | 50.00% | 20.00% | 10.00% | 2.00% |
| 20 | 100.00% | 40.00% | 20.00% | 4.00% |
| 50 | 250.00% | 100.00% | 50.00% | 10.00% |
The same absolute deviation implies very different relative variability.