Coefficient of Variation Calculator

StatisticsLast updated: August 22, 2026

The coefficient of variation (CV) is the standard deviation divided by the mean, usually written as a percentage. Because it carries no unit, it lets you compare series measured on different scales or in different units: a standard deviation in kilograms cannot be set against one in centimeters, but their coefficients of variation can.

This calculator evaluates one or two data sets together. For each series it reports the mean, the standard deviation, the coefficient of variation, an approximate standard error for that coefficient, and a homogeneity reading; when a second series is entered, it states plainly which one is more homogeneous and reports the CV ratio and the difference in points. A comparison table, a bar chart, and a box plot back the results up.

The first series of the comparison. Values can be separated by commas, spaces, or line breaks.
This name is used in the results and the charts.
Enter a second series to compare the variability of the two. They do not have to share a unit.
Ignored when the second series is empty.
Sets the denominator of the standard deviation, and the CV follows directly from that deviation.

Coefficient of Variation Formulas

For a sample:      CV = s / |x̄|        s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
For a population:  CV = σ / |μ|        σ = √[ Σ(xᵢ − μ)² / n ]
As a percentage:   CV(%) = (s / |x̄|) · 100
Standard error:    SE(CV) ≈ CV / √(2n)
Comparison:        CV₁ < CV₂  ⇒  series 1 is relatively more homogeneous
Inverse measure:   signal-to-noise ratio = x̄ / s = 1 / CV

The coefficient of variation is also known as the relative standard deviation (RSD). In Excel, =STDEV.S(range)/AVERAGE(range) gives the same value, as does the Std. Deviation / Mean ratio from the SPSS Descriptives output.

How to Calculate

  1. Paste your first data set into the box and, if you like, give the series a name.
  2. If you want a comparison, enter the second data set as well; the two do not have to share a unit.
  3. Choose whether the data is a sample or a population — this sets the denominator of the standard deviation and therefore the CV.
  4. Read the coefficient of variation as a percentage: it says what percentage of the mean the standard deviation amounts to.
  5. If you entered two series, look at the 'more homogeneous series' card and the CV ratio; a lower CV means a more consistent measurement.
  6. Make sure the mean is not close to zero and that the data is on a ratio scale; otherwise the CV is misleading.

Worked Examples

Comparing the variability of height and weight

The height series has a mean of 172.10 cm and a standard deviation of 4.48 cm, giving CV = 2.61%; the weight series has a mean of 70.80 kg and a standard deviation of 11.10 kg, giving CV = 15.68%. The standard deviations are in different units and cannot be compared directly, but the coefficients of variation show that weight is roughly 6.02 times as variable as height.

Boy (cm) — Coefficient of variation (CV): 2.61% · Boy (cm) — Homogeneity: Very homogeneous · Boy (cm) — Number of values (n): 10

Homogeneity of a single series

Eight fill-weight measurements have a mean of 50 g and a sample standard deviation of 2 g, so CV = 4.00%. Being below 10%, this value shows that the production line runs very homogeneously. The approximate standard error of the CV is 1.00%, which puts the rough 95% confidence interval at 2.04% – 5.96% — so the true value is expected to stay below the 10% mark as well.

Coefficient of variation (CV): 4.00% · Homogeneity: Very homogeneous · Number of values (n): 8

Stability of two production lines

Line A has a mean of 120.75 and a standard deviation of 2.82, giving CV = 2.33%; line B has a mean of 312.88 and a standard deviation of 24.47, giving CV = 7.82%. Line B's standard deviation is numerically far larger (24.47 against 2.82), but its production level is higher too; even so, its relative variability is 3.35 times that of line A, so line A is the more stable of the two.

A hattı — Coefficient of variation (CV): 2.33% · A hattı — Homogeneity: Very homogeneous · A hattı — Number of values (n): 8

Frequently Asked Questions

What is the coefficient of variation good for?
By expressing the standard deviation as a proportion of the mean it becomes unitless, which makes the variability of series on different scales comparable. In a series with a mean of 5 a deviation of 1 unit is large; in one with a mean of 500 the same deviation is negligible, and the CV captures exactly that difference. It is the standard reporting measure for laboratory repeatability, production stability, and agricultural trial results.
How high does the coefficient of variation have to be to count as high?
The general convention is that below 10% is very homogeneous, 10–20% homogeneous, 20–30% moderate, and above 30% heterogeneous. The cutoffs vary by field, though: in analytical chemistry even 5% can be considered high, while in the social sciences 40% may be routine. So interpret the CV by comparison with similar studies in the same field rather than against an absolute threshold.
When should the coefficient of variation not be used?
Not for interval-scale variables (Celsius temperature, calendar year, IQ score), because zero is arbitrary on those scales and the ratio is meaningless. The CV explodes for series whose mean is near zero, and it cannot be interpreted for series containing both negative and positive values because of the sign problem. In those cases report the standard deviation directly, or the IQR.
Can the difference between two CVs be tested statistically?
Yes; methods such as the Feltz-Miller test or the modified Bennett test examine the equality of two or more coefficients of variation. In practice, a direct comparison of the CVs is enough for most reports. For a rough idea, build confidence intervals from the standard errors given by CV/√(2n) and check whether they overlap.
Should I pick the sample or the population standard deviation?
If your data is a sample drawn from a larger population, choose the sample formula with the n−1 denominator; that is the default for research data. The population formula can be used if you are only describing the group you measured and will not generalize. In small samples, the choice changes the CV noticeably.
How do I compute the coefficient of variation in Excel?
There is no ready-made function; write =STDEV.S(range)/AVERAGE(range) and format the cell as a percentage. Use STDEV.P for the population formula. SPSS does not show it in the Descriptives output directly — it comes from the Ratio Statistics menu or from the Std. Deviation / Mean pane; in R, sd(x)/mean(x) is all you need.
Is the CV related to the signal-to-noise ratio?
Yes, the signal-to-noise ratio is the reciprocal of the coefficient of variation: x̄/s = 1/CV. Engineering wants a high signal-to-noise ratio while statistics wants a low CV; the two express the same information from opposite directions. Reading the CV as 'the relative noise of the measurement' therefore makes it easier to interpret.