Coefficient of Variation Calculator

How to use the calculator

Pick what you know under Calculate from:

• Enter summary data: type the standard deviation and the mean of your sample. Neither may be zero.
• Enter raw data, means: paste the observations separated by spaces, commas, tabs or new lines. The calculator finds the mean and the sample standard deviation (dividing by n − 1) for you and needs at least two values.
• Enter raw data, proportions: for yes/no outcomes such as a conversion rate, give the sample size and the event proportion. You can enter it as a proportion (0.05), a percentage (5%) or a count of events (50).

The result is shown twice: as a plain ratio, for example 0.263523, and as a percentage, 26.35%. A negative mean gives a negative CV; the magnitude is what matters.

What is the coefficient of variation?

The coefficient of variation (CV), also called the relative standard deviation (RSD), is the standard deviation divided by the mean. It has no unit, so it lets you compare how much two quantities vary even if one is measured in grams and the other in kilometres, or if one has a much larger average than the other.

A standard deviation of 10 means something very different for a mean of 20 than for a mean of 2,000. The CV makes that visible: 10 ÷ 20 is 50%, while 10 ÷ 2,000 is 0.5%. A lower CV means the values cluster tightly around the mean in relative terms.

Formula for the coefficient of variation

CV = s ÷ x̄s is the standard deviation and x̄ the mean. Multiply by 100 for a percentage.

When you paste raw data the calculator uses the sample standard deviation, s = √[ Σ (xᵢ − x̄)² ÷ (n − 1) ]. If you already have a standard deviation from elsewhere, check whether it was computed for a sample or a whole population; use the standard deviation calculator to get either.

For a proportion p estimated from n independent observations, the standard error is √[p(1 − p) ÷ n], so the relative standard error of the estimate is:

CV(p̂) = √[ (1 − p) ÷ (n × p) ]The coefficient of variation of an observed proportion; it shrinks as n grows and as p moves toward 1.

Worked examples

From raw data. Take the five readings 12, 15, 18, 21 and 24. The mean is 90 ÷ 5 = 18. The deviations are −6, −3, 0, 3 and 6, whose squares add up to 90. Dividing by n − 1 = 4 gives a variance of 22.5 and a standard deviation of 4.7434. So CV = 4.7434 ÷ 18 = 0.263523, or 26.35%.

Comparing two groups. Group A has a mean of 50 and a standard deviation of 5, so its CV is 10%. Group B has a mean of 200 and a standard deviation of 10, so its CV is 5%. Group B has the larger standard deviation but is the less variable of the two once its bigger mean is taken into account.

A proportion. A page converts 20% of 500 visitors. The standard error of the rate is √(0.2 × 0.8 ÷ 500) = 0.0179, and dividing by 0.2 gives a CV of 0.0894, or 8.94%. Entering 0.2 with a sample size of 500 in the calculator returns the same value.

When the CV is appropriate

• Use it for ratio-scale data, where zero means "none" and ratios are meaningful: weights, lengths, durations, concentrations, prices.
• Avoid it for interval scales such as temperature in Celsius or Fahrenheit. Their zero is arbitrary, so shifting the scale changes the mean and therefore the CV without changing the spread.
• Be careful when the mean is close to zero. The CV becomes huge and unstable, and the calculator refuses a mean of exactly zero.
• It is common in laboratory work to report precision (the CV of repeated measurements), in finance to compare risk per unit of return, and in quality control to monitor consistency.
• With very small samples the CV tends to be biased low, so a figure from five or ten observations is only a rough guide.

A CV of 0.25 and a CV of 25% are the same thing, so check which form a report is quoting. The calculator shows both so you can copy whichever you need.