Foundations · Spread
Coefficient of Variation Calculator
Which of these is more variable — relative to its own size? The coefficient of variation expresses the standard deviation as a percentage of the mean, stripping out the units so you can compare the spread of things measured on completely different scales. Enter one dataset, or several (one per line), to rank them by relative variability.
Each line is treated as a separate dataset. With one line you get the full detail; with several, a comparison ranked by CV. The CV only makes sense for positive, ratio-scaled data (lengths, weights, prices) — not for things like temperature in °C.
Result
In plain English
A standard deviation of 10 is large for shoe sizes and tiny for house prices — its meaning depends entirely on the scale. The coefficient of variation fixes that by dividing the standard deviation by the mean, giving a unit-free percentage. A CV of 15% means the typical wobble is 15% of the average, whatever the units, so two utterly different quantities can be put on the same yardstick of relative variability.
- coefficient of variation (CV)
- The standard deviation as a fraction of the mean: SD ∕ mean, usually written as a percentage. Higher = more spread relative to the average.
- relative vs absolute spread
- The SD is absolute spread in the original units; the CV is relative spread, scaled to the mean. A group can have a larger SD yet a smaller CV than another, or the reverse.
- when it is valid
- Only for ratio data with a true, meaningful zero and a positive mean — lengths, weights, counts, prices. It is meaningless for interval scales like Celsius, where zero is arbitrary.
- the danger near zero
- As the mean approaches zero the CV explodes, and if the mean can be negative it becomes nonsense. The CV is only stable when the mean is safely positive.
- also called
- Relative standard deviation (RSD), especially in chemistry and lab work, where it gauges the precision of a measurement.
Frequently asked
How do you calculate the coefficient of variation?
Divide the standard deviation by the mean, then multiply by 100 to get a percentage: CV = (SD ∕ mean) × 100. For a sample with mean 72.5 and standard deviation 10.9, the CV is (10.9 ∕ 72.5) × 100 ≈ 15%. Use the sample standard deviation (÷ n − 1) for sample data. The result is unit-free, which is the whole point — it lets you compare variability across different scales.
What is a good or high coefficient of variation?
There is no universal threshold — it depends on the field. In a precise laboratory assay a CV above a few percent may be unacceptable; for stock returns or biological measurements, 20–30% is routine. The CV is most useful for comparison: a higher CV means more relative variability than a lower one. Judge it against a benchmark in your own domain, not an absolute cut-off.
What is the difference between the CV and the standard deviation?
The standard deviation measures spread in the data’s own units, so its size depends on the scale; the coefficient of variation divides that by the mean to give a unit-free percentage. Use the SD to describe the spread of one dataset; use the CV to compare the spread of two or more datasets measured on different scales or in different units. A bigger SD does not always mean a bigger CV.
When should I not use the coefficient of variation?
Avoid it when the data are not on a ratio scale (a true zero), when the mean is near zero or can be negative — where the CV blows up or turns meaningless — and when comparing things measured on genuinely incomparable scales. Temperature in Celsius is the classic trap: because 0 °C is arbitrary, its CV changes if you switch to Fahrenheit or Kelvin, so the number means nothing.