ToolForage.
STATISTICS CALCULATOR

Coefficient of Variation Calculator

Enter a positive mean and standard deviation for each dataset to compare their coefficients of variation.

Calculator

YOUR RESULTS
Dataset A coefficient of variation10 %
Dataset B coefficient of variation
7.5 %
Absolute CV gap
2.5 percentage points
Lower relative spread
Dataset B

Relative spread on a common percentage scale

  • Dataset A coefficient of variation10 %
  • Dataset B coefficient of variation7.5 %

A lower CV means a smaller standard deviation relative to its mean, not automatically a better dataset.

Understanding your result

CV expresses standard deviation as a percentage of the mean. The gap is in percentage points. Dataset names identify the lower relative spread, without making a quality or significance judgment.

If you have raw observations rather than summary statistics, first use the Standard Deviation Calculator .

The formula

Coefficient of variation (%) = standard deviation ÷ mean × 100. CV gap = |CV(A) − CV(B)|.

Dividing by the mean removes the measurement unit. Use a sample standard deviation with a sample mean, or population quantities together. This tool accepts those summaries rather than guessing which standard-deviation convention was used.

Worked example

Dataset A with mean 100 and standard deviation 10 has CV 10%. Dataset B with mean 200 and standard deviation 15 has CV 7.5%. B has a larger absolute standard deviation but a smaller relative spread, by 2.5 percentage points.

How to use this calculator

  1. Calculate each dataset’s mean and matching standard deviation.
  2. Confirm that both means are positive and the measurement scales have meaningful zeros.
  3. Enter the summaries and compare the CV percentages and gap.

A meaningful zero matters

CV is most interpretable on a ratio scale, where zero represents absence of the quantity. Changing a length from metres to centimetres multiplies both its mean and standard deviation by the same factor, leaving CV unchanged. Converting Celsius to Fahrenheit also adds an offset, so it can change CV without changing the physical variation. That makes CV unsuitable for such an offset-based comparison.

Avoid treating CV as a universal quality score

A very small positive mean can create an enormous CV. Consider whether the mean is a stable and meaningful baseline before interpreting the ratio. Different sample sizes, outliers, and measurement processes can also affect the comparison. A lower CV alone does not establish a statistically significant difference, better accuracy, or a more desirable outcome.

Assumptions & limitations

What this calculation assumes

  • Both means are strictly positive and the input standard deviations match their datasets.

What to keep in mind

  • No raw-data parsing, sample-size adjustment, significance test, or lognormal-specific estimator.
  • Zero or negative means are excluded because this tool targets positive ratio-scale comparisons.

Common questions

Is CV the same as standard deviation?

No. Standard deviation has the original measurement unit; CV divides it by the mean to describe relative spread.

Is relative standard deviation the same result here?

For the positive means supported here, the usual percentage relative standard deviation equals the displayed CV. Conventions involving negative means are outside this tool’s scope.

Sources & further reading