Coefficient of Variation Calculator
The coefficient of variation (CV) is the standard deviation expressed as a percentage of the mean. It measures how large the variability is relative to the typical value, which makes it far more informative than the raw standard deviation when you are comparing two data sets with different scales or units. If one investment has a mean return of 10% with a standard deviation of 2%, and another has a mean return of 100% with a standard deviation of 15%, the second investment has a larger absolute standard deviation but a smaller CV (15% versus 20%), meaning its return is actually more stable relative to what you expect. This is why the CV is sometimes called the relative standard deviation (RSD) and is widely used in finance, quality control, laboratory science, and ecology. The formula is straightforward: CV = (standard deviation / mean) times 100. The sign of the mean matters: the CV is only meaningful when the mean is a positive number. When the mean is zero or negative, the CV is undefined or misleading. This calculator offers two modes. In mean and SD mode, you enter the mean and standard deviation directly. In raw data mode you enter a comma-separated list of values and the calculator computes the sample standard deviation and mean for you. Both modes return the CV as a percentage, the mean, the standard deviation, and a plain-language variability label based on common conventions. Two data values are required in raw data mode. The tool is useful for students, analysts, scientists, and anyone comparing the spread of two or more data sets where a fair comparison requires scaling for the level of the data.
How it works
In manual mode, CV = (SD / mean) x 100. In raw data mode, the sample mean is the sum of all values divided by n, and the sample standard deviation uses n minus 1 in the denominator (Bessel's correction). CV is then computed the same way. The variability label applies the convention: CV below 10% is low, 10-20% moderate, above 20% high. If the mean is zero or negative, the result is shown as N/A since the CV is not meaningful.
Worked example
Mean = 50, SD = 10. CV = (10 / 50) x 100 = 20.00%. A CV of 20% is classified as moderate variability: the standard deviation is one fifth of the mean. These match the default values pre-filled above. In raw data mode, entering 40, 45, 50, 55, 60 gives the same mean of 50 and sample SD of approximately 7.91, producing a CV of about 15.81%.
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