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Coefficient of Variation Calculator

The coefficient of variation (CV) expresses standard deviation as a percentage of the mean: CV = SD / mean x 100. Paste a list of values and choose Sample or Population, or enter a mean and a standard deviation you already have. For 12, 15, 9, 14, 20, the mean is 14: the sample CV is 29.01% and the population CV is 25.95%. This page labels the basis, shows the other basis for the same list, and substitutes your mean and SD into the formula. It accepts up to 10,000 values from a spreadsheet column and uses centred sums to reduce numerical cancellation. CV is meaningful for data on a ratio scale with a meaningful zero and a positive mean. A mean at or below zero is reported as undefined, and a mean close to zero can make the percentage unstable.

CV29.01%mean 14 · sample SD 4.0620 · n = 5 · SD / mean x 100
CV
29.01%
Mean
14
SD (sample)
4.0620
Basis
Sample
Where the numbers come from
Which standard deviation

Use the sample basis when these values are a sample drawn from something larger. Dividing by n - 1 rather than n corrects the tendency of a sample to look tighter than the population it came from, so the figure is slightly larger.

The sample standard deviation of 5 values is 4.0620 and the mean is 14, so the coefficient of variation is 29.01%. CV = 4.0620 / 14 x 100 = 29.01%

On the population basis, which divides by n, the same values give SD 3.6332 and CV 25.95%.

Commas, spaces, tabs, semicolons and new lines all separate values, so a column copied from a spreadsheet pastes straight in, and up to 10,000 values are read at a time. Figures are shown to four decimal places and percentages to two; the arithmetic itself keeps full double precision. Nothing you type leaves this browser.

Worked examples

The three cases a coefficient of variation usually starts from. Every figure here is computed by the same code as the answer above, so an example and the tool can never disagree.

  • Mean 100, SD 15given directly
    15.00%
  • 12, 15, 9, 14, 20sample basis
    29.01%
  • Mean 0the ratio has no denominator
    undefined, the mean is 0
When the percentage stops meaning anything. A coefficient of variation is the spread as a share of the mean, so it needs a mean above zero on a scale where zero is a true zero: lengths, weights, counts, prices. At a mean of 0 there is nothing to divide by and below zero the sign flips, so both come back here as undefined rather than as a figure. Temperature in Celsius has an arbitrary zero, so its coefficient of variation is not a meaningful relative spread. Zero values alone do not invalidate the ratio on a scale with a meaningful zero, but a mean close to zero can make it unstable. Above 100% the standard deviation is larger than the mean; that percentage alone does not determine whether a comparison is useful.
Accuracy. Uses double-precision arithmetic, compensated centred sums and a scaled deviation norm when squared totals are outside the numerical range. Nonzero input, mean, spread or percentage that rounds to zero is refused rather than reported as no variation. Extreme magnitudes can also exceed the numerical range. The sample or population basis is named, and a mean at or below zero is reported as undefined.

Common questions

How do I calculate the coefficient of variation?
Divide the standard deviation by the mean and multiply by 100. For 12, 15, 9, 14, 20 the mean is 14 and the sample standard deviation is 4.0620, so the coefficient of variation is 29.01%. The page prints that substitution under the answer with your own figures in it, so a number typed into the wrong box is easy to spot, and it reports the result as a percentage because the ratio itself is unitless: the units of the spread and the units of the mean cancel.
Should I use the sample or the population standard deviation?
Use the sample basis when your values are a sample drawn from something larger, and the population basis when they are the whole group you care about. The difference is the divisor: n - 1 against n. It is not a rounding detail. The same five values, 12, 15, 9, 14, 20, give 29.01% on the sample basis and 25.95% on the population basis, because the sample standard deviation is 4.0620 and the population standard deviation is 3.6332. This page labels which one produced the figure and prints the other beside it, so the two are never confused.
Can the coefficient of variation be negative or undefined?
It has no value at all when the mean is zero, because there is nothing to divide by, and it is meaningless when the mean is negative, because the sign of the ratio then says something about the sign of the mean rather than about the spread. This page reports both as undefined and says which case it is, rather than printing a negative percentage or a division that looks like a figure. The mean and the standard deviation are still shown, since those remain perfectly well defined.
Why is my coefficient of variation enormous?
The mean is small compared with the standard deviation. Since the mean is the denominator, a mean close to zero can make the ratio very sensitive to changes in the data. A CV above 100% means the standard deviation exceeds the mean; that is not, by itself, a universal cutoff for a valid comparison. Check the measurement scale and the context before interpreting relative spread.
Can I use it on data that includes negative values?
The page computes a CV when the mean is positive and flags lists containing zero or negative values. Interpretation requires a ratio scale with a meaningful zero. Temperature in Celsius has an arbitrary zero, so its CV is not a meaningful relative spread. A zero observation on a ratio scale, such as a count of zero, does not by itself invalidate CV. A mean close to zero can still make the ratio unstable.
Do I need the raw data, or can I enter a mean and a standard deviation?
Either. Choose From a mean and an SD to enter those two figures directly. A mean of 100 with a standard deviation of 15 gives a coefficient of variation of 15.00%. The basis is labelled As given because the supplied SD already has its sample or population basis. Variance, probability weights and frequency tables are not accepted as inputs in that mode.
How many values can I paste, and how are they read?
Up to 10,000 values and 200,000 characters in one paste. Commas, spaces, tabs, semicolons and new lines separate values, so a numeric spreadsheet column can be pasted directly. Currency symbols and accounting parentheses are read. A comma always separates values in the list: 1,234 is read as 1 and 234, with a note explaining the reading. Remove thousands commas from individual list values before pasting. Invalid entries are named rather than silently skipped, and out-of-range values are refused. A nonzero number too small to represent is refused with its original spelling and instructions to scale the values up; genuine zero spellings remain valid.
How accurate is the standard deviation on large numbers?
The calculation subtracts the mean, uses compensated centred sums and corrects for residual drift. If direct squared totals leave the numerical range, it computes the SD from scaled centred deviations instead of treating tiny unequal values as no spread. For 1000000004, 1000000007, 1000000013 and 1000000016, the centred calculation gives sample variance 30. Arithmetic still uses double precision. Nonzero tokens that would convert to zero are named and refused; unrepresentable means, SDs and positive percentages are reported as numerical limits. Scale all observations, or a supplied mean and SD together, by the same positive factor to change units. A final percentage outside the representable range needs a higher-precision calculation because changing units leaves CV unchanged.
What is a good coefficient of variation?
There is no universal good or bad threshold. CV describes the size of the standard deviation relative to a positive mean on a ratio scale. A smaller percentage means less relative spread in those supplied numbers, but interpreting a comparison also requires the measurement context. This calculator supplies descriptive arithmetic; it does not classify measurement quality or choose an action.
How can I work through the calculation step by step?
First find the mean. For 12, 15, 9, 14, 20, the sum is 70 and the mean is 70 / 5 = 14. The deviations are -2, 1, -5, 0, 6; their squares total 66. Divide 66 by 4 for sample variance, then take the square root to get SD 4.0620. Finally, 4.0620 / 14 x 100 gives 29.01%. For the population basis, divide 66 by 5 instead, giving SD 3.6332 and CV 25.95%. The calculator shows the mean, SD, basis and CV substitution for your list; it does not display a separate row for every deviation.
What does CV mean, and why is the result a percentage?
CV is short for coefficient of variation. The ratio SD / mean has no units because the SD and mean use the same units. This page multiplies that ratio by 100 to display a percentage. A mean of 100 and SD of 15 therefore gives a ratio of 0.15, displayed as 15.00%. The CV label identifies the result here; symbols and key sequences on other calculators depend on their model.
Can I enter grouped data or probabilities?
This calculator accepts individual observations, or a supplied mean and SD. It has no separate frequency, class-interval or probability column. Pasting a two-column table would treat both columns as observations rather than as values and weights, so it would compute a different quantity. Class midpoints alone also omit the frequencies. Use the individual observations or summary figures only when they already describe the intended dataset.
How do I calculate the same coefficient in Excel?
For a numeric range A1:A5 with a positive mean, use =STDEV.S(A1:A5)/AVERAGE(A1:A5)*100 for the sample percentage, or replace STDEV.S with STDEV.P for the population percentage. Display that result as an ordinary number. If the cell is formatted as a percentage, omit *100 so the format does the conversion. These formulas describe a separate Excel workflow; this page calculates from pasted values and does not open or edit a workbook.

Uses double-precision arithmetic, compensated centred sums and a scaled deviation norm when squared totals are outside the numerical range. Nonzero input, mean, spread or percentage that rounds to zero is refused rather than reported as no variation. Extreme magnitudes can also exceed the numerical range. The sample or population basis is named, and a mean at or below zero is reported as undefined.