Coefficient of Variation Calculator (CV / RSD, with Steps)
Compute the coefficient of variation (CV, or relative standard deviation) from a mean and standard deviation, or paste raw data. Get sample and population CV, the small-sample unbiased CV, a confidence interval for the CV, a two-set comparison and the full working.
How it works
CV = SD ÷ |mean| × 100% (sample: s ÷ |x̄|, population: σ ÷ |μ|) · Unbiased CV ≈ (1 + 1 ÷ 4n) × CV · CI (Vangel modified McKay): K ÷ √[((u + 2) ÷ n − 1) K² + u ÷ (n − 1)] with u = χ²(1 − α/2) for the lower and χ²(α/2) for the upper limit, K = s ÷ x̄
The coefficient of variation expresses the standard deviation as a percentage of the mean, which gives a unitless measure of relative spread. It is also called the relative standard deviation (RSD). Because it strips out the scale, you can compare the consistency of data sets with different units or very different averages. Enter a mean and standard deviation, or paste raw data. With raw data the calculator works out the mean and both the sample and population standard deviations, and the Sample/Population switch picks which one the CV uses. If you give the sample size, you also get the small-sample unbiased CV and a confidence interval for the CV. The interval uses Vangel’s modified McKay method, which is based on the chi-square distribution and assumes roughly normal data. To compare two sets, choose a comparison mode. The two CVs, their intervals and a side-by-side table show which set is more consistent. The CV only makes sense on a ratio scale, with a meaningful zero and positive values. A mean near zero makes the ratio blow up.
Worked example
A data set with mean 50 and standard deviation 10 has CV = 10 ÷ 50 × 100 = 20%. A second set with mean 500 and standard deviation 50 has CV = 50 ÷ 500 × 100 = 10%. Its raw spread is five times larger, yet it is more consistent relative to its size. With raw data such as five guesses of 80, 88, 76, 88 and 91, the mean is 84.6. The squared deviations add up to 159.2, so the sample SD is √(159.2 ÷ 4) = 6.3087 and CV = 6.3087 ÷ 84.6 = 7.46%. The unbiased CV is (1 + 1 ÷ 20) × 7.46% = 7.83%, and the 95% confidence interval for the CV is about 4.46% to 21.68%.
Sources: NIST/SEMATECH e-Handbook of Statistical Methods — measures of scale · Vangel, M. G. (1996), Confidence Intervals for a Normal Coefficient of Variation — The American Statistician 50(1)
Frequently asked questions
When is the CV more useful than the standard deviation?
When you compare spread across data measured differently, such as weight in grams versus pounds, or salaries versus test scores. The raw standard deviations aren’t comparable, but the CV percentages are. Use a comparison mode to put two sets side by side.
Why can’t I use the CV when the mean is near zero?
Dividing by a mean close to zero produces a huge, unstable CV, and with a negative mean the sign means nothing. The CV is reserved for ratio-scale data with a positive mean, such as heights, prices or reaction times. Don’t use it for temperatures in °C or °F.
What counts as a high coefficient of variation?
It depends on the field. A rough guide: under about 15% is low variability, 15–30% is moderate, and above 30% is high. Laboratory assays often aim for under 10–15%. Always judge it against the norms for your measurement.
Should I use the sample or the population CV?
Use the sample CV (with s, dividing by n − 1) when your numbers stand in for a larger group, which is the usual case. Use the population CV when you have every member of the group. With raw data the calculator shows both.
What is the unbiased CV?
The ordinary sample CV slightly underestimates the true CV in small samples. Multiplying by (1 + 1 ÷ 4n) corrects most of that bias. With n = 5 that is a 5% increase, and with n = 100 only 0.25%.
How is the confidence interval for the CV calculated?
With Vangel’s modified McKay method. It turns chi-square quantiles for n − 1 degrees of freedom into lower and upper limits for the CV, and it assumes roughly normal data. Small samples give wide intervals: five values with a CV near 7.5% give a 95% interval of about 4.5% to 22%.
Related calculators
For education — check assumptions (sample size, distribution) before using statistics in real decisions.