Coefficient of Variation Calculator
Choose whether to type your values or a known mean and standard deviation. The coefficient of variation is the standard deviation as a percentage of the mean, which lets you compare spread across different scales.
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Formula
CV% = standard deviation ÷ |mean| × 100
When you enter values, the mean is Σx ÷ n and the standard deviation is sqrt( Σ(x - mean)² ÷ d ), where d = n - 1 for a sample and d = n for a population. In mean-and-SD mode your two numbers are used directly.
Worked example
Values 2, 4, 4, 4, 5, 5, 7, 9 (n = 8) have mean 5 and Σ(x - mean)² = 32.
- Population: SD = sqrt(32 ÷ 8) = 2, so CV = 2 ÷ 5 × 100 = 40%
- Sample: SD = sqrt(32 ÷ 7) = 2.1381, so CV = 42.76%
- Summary mode: mean 50 and SD 5 give 5 ÷ 50 × 100 = 10%
A mean of exactly 0 returns an error because the CV would be undefined. A negative mean is handled by using its absolute value.
Frequently asked questions
What is the coefficient of variation?
The coefficient of variation (CV), also called relative standard deviation, is the standard deviation divided by the absolute value of the mean, times 100. A mean of 50 with a standard deviation of 5 gives a CV of 10%.
Should I use the sample or population standard deviation?
Use sample when your values are a subset of a larger group, and population when they are every value. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5; the population SD is 2 (CV 40%) and the sample SD is 2.138 (CV 42.76%).
What is a good or acceptable CV?
It depends on the field. Lower means more consistent data relative to the mean. Many lab methods look for a CV under 10 to 15%, but there is no universal limit.
Why is the CV undefined when the mean is 0?
The CV divides by the mean, so a mean of 0 gives an undefined result, and values near 0 make it unstable. Values such as -1 and 1 have mean 0, so no CV can be shown.
How is a negative mean handled?
This calculator divides by the absolute value of the mean, so the CV is never negative. A mean of -50 with an SD of 5 also gives 10%. CV is meant for ratio-scale data with a true zero, such as weights or counts.