Coefficient of variation calculator
CV = standard deviation divided by the mean, times 100. It compares spread across different scales, but it only makes sense when the mean is well away from zero.
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Coefficient of Variation Calculator
The coefficient of variation is the standard deviation divided by the mean, expressed as a percent, giving a unit free measure of relative spread.
Standard deviation alone cannot tell you whether spread is large or small relative to the size of the values. The coefficient of variation fixes that by dividing the standard deviation by the mean: CV = (SD / mean) * 100. Because both numbers share the same units, the units cancel and the result is a pure percentage. That makes CV the standard tool for comparing variability across datasets with different scales, such as the consistency of two machines that fill 250 ml and 2 liter bottles.
CV has one hard limit: it divides by the mean, so it breaks down when the mean is zero or close to it. This calculator detects that case and shows a warning instead of a number. For the standard deviation and variance themselves, use the standard deviation solver or the variance calculator, both of which show the full working from raw data.
The tool runs entirely in your browser with plain JavaScript. Nothing you type leaves your device.
Worked example
A production line fills bags with a mean weight of 20 grams and a standard deviation of 5 grams. What is the coefficient of variation?
Step 1, divide the standard deviation by the mean: 5 / 20 = 0.25.
Step 2, convert to a percent: CV = 0.25 * 100 = 25 percent. The typical bag deviates from the mean by about a quarter of the mean's size, which counts as moderate relative variability by the usual rule of thumb. Enter 5 and 20 in the calculator above and you will see exactly this result with the same steps.
Frequently asked questions
What is the coefficient of variation?
The coefficient of variation, or CV, is the standard deviation divided by the mean, usually expressed as a percent: CV = (SD / mean) * 100. It measures spread relative to the size of the values, which makes it unit free. A CV of 25 percent means the standard deviation is one quarter of the mean.
Why use the coefficient of variation instead of the standard deviation?
Standard deviation is measured in the same units as the data, so it cannot fairly compare spread across different scales or units. A standard deviation of 5 is huge for data centered near 10 and tiny for data centered near 10,000. Dividing by the mean removes the scale, so CV lets you compare the relative variability of things like stock returns, lab measurements, and incomes on one scale.
What happens when the mean is zero or close to zero?
The CV divides by the mean, so a mean of zero makes it undefined and a mean near zero makes it explode to a huge, unstable number that says nothing useful. Data that straddle zero, like temperature changes or profit-and-loss figures, are a poor fit for CV. This calculator shows a clear warning instead of a result in that situation.
What counts as a high coefficient of variation?
A rough rule of thumb: under 10 percent is low relative variability, 10 to 30 percent is moderate, and above 30 percent is high. Context matters more than the cutoff. A CV of 20 percent is excellent consistency for agricultural yields but would be alarming for a precision machining process.
Can the mean be negative?
Mathematically the formula still runs, but a negative mean flips the sign of the CV and muddies interpretation. The common convention is to take the absolute value of the mean when the data are signed, or better, to avoid CV entirely for data that cross zero. This calculator reports the signed result with a note when the mean is negative.
Should I use the sample or population standard deviation in the CV?
Match the standard deviation to your data: sample SD (divide by n - 1) when generalizing from a sample, population SD (divide by n) when your list is the whole group. The homepage solver computes both from raw numbers, and the sample versus population guide explains the difference.