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To calculate the coefficient of variance in Excel, divide the standard deviation by the mean: =STDEV.S(A2:A11)/AVERAGE(A2:A11), then format the cell as a percentage. Excel has no single built-in coefficient-of-variation function, so the ratio is built from two functions you already have. The choice that changes your answer is STDEV.S (sample) versus STDEV.P (whole population); on Microsoft’s own example data it moves the result from 2.07% to 1.96%. (Statisticians say “coefficient of variation”; “coefficient of variance” is the common search spelling for the same quantity.)
What the coefficient of variance is used for in research
The coefficient of variation (CV) expresses spread relative to the mean, so you can compare the variability of measurements that sit on different scales, such as replicate readings from two assays. NIST’s Dataplot reference defines it as the sample standard deviation divided by the sample mean, and cautions that it should typically only be used for data measured on a ratio scale, that it depends on the measurement scale (Celsius and Fahrenheit give different values), and that it becomes unstable when the mean is near zero. For the concept itself, interpretation and field benchmarks, see the coefficient of variation guide; this page covers only the Excel mechanics. If you are unsure whether your variable is on a ratio scale, read levels of measurement first.
Install or access
Nothing to install. STDEV.S, STDEV.P, VAR.S, VAR.P and AVERAGE are built-in worksheet functions, documented on Microsoft Support. The Analysis ToolPak is not needed for this calculation; the related Excel statistics functions guide covers when the ToolPak is useful.
How to calculate the coefficient of variance in Excel, step by step
The worked example uses the breaking-strength data from Microsoft’s STDEV.S function page: ten values entered in A2:A11.
| Cell | Value |
|---|---|
| A2 | 1345 |
| A3 | 1301 |
| A4 | 1368 |
| A5 | 1322 |
| A6 | 1310 |
| A7 | 1370 |
| A8 | 1318 |
| A9 | 1350 |
| A10 | 1303 |
| A11 | 1299 |
- Enter the data in a single column with no text labels inside the range (a header above the range, in A1, is fine).
- Find the mean. In an empty cell type
=AVERAGE(A2:A11). Result: 1328.6. - Find the standard deviation. If the ten values are a sample from a larger set of measurements, type
=STDEV.S(A2:A11). Result: 27.46391572 (the value Microsoft’s page gives).STDEV.Suses the n-1 method. - Divide. In a new cell type
=STDEV.S(A2:A11)/AVERAGE(A2:A11). Result: 0.020671. - Show it as a percentage. Select the cell and choose Percentage in the Number group on the Home tab (or press Ctrl+Shift+%). The cell now reads 2.07%. Alternatively multiply by 100 in the formula:
=STDEV.S(A2:A11)/AVERAGE(A2:A11)*100.
Sample or population: which standard deviation?
Use STDEV.S when your data are a sample and STDEV.P when they are the entire population. Microsoft’s pages give the same example data both ways, and the CV follows:
| Formula | Standard deviation (Microsoft Support) | CV with mean 1328.6 |
|---|---|---|
=STDEV.S(A2:A11)/AVERAGE(A2:A11) |
27.46391572 | 2.07% |
=STDEV.P(A2:A11)/AVERAGE(A2:A11) |
26.05455814 | 1.96% |
Microsoft’s STDEV.P page presents its figure as the result when only 10 tools are produced, that is, when the ten values are the whole population. Most replicate-measurement work treats the data as a sample, so STDEV.S is the usual choice; whichever you pick, state it when you report the CV. The difference between the two is the same n versus n-1 distinction explained in how to find population variance.
Optional: the small-sample correction
NIST’s Dataplot reference gives an approximately unbiased estimate for normally distributed data as (1 + 1/(4n)) times the CV. Typed as an Excel formula (our translation of NIST’s expression): =(1+1/(4*COUNT(A2:A11)))*STDEV.S(A2:A11)/AVERAGE(A2:A11). For the example data (n = 10) this factor is 1.025 and moves 2.07% to about 2.12%; the correction matters mainly for small n.
Output and how to read it
A CV of 2.07% means the sample standard deviation is about 2% of the mean breaking strength. It describes relative dispersion only. It is not an error rate and does not say whether the spread is acceptable; that depends on your field and measurement method. NIST also notes the CV cannot be used to build a confidence interval for the mean. Report the CV together with n, the mean and which standard deviation you used.
Troubleshooting
| What you see | Why (per Microsoft Support) |
|---|---|
| Result is slightly different from a colleague’s | STDEV.S assumes a sample (n-1); STDEV.P assumes the entire population (n). Check which was used. |
| A number stored as text is ignored and n is smaller than expected | In a cell reference or range, text is skipped by STDEV.S, STDEV.P and AVERAGE, so those cells silently drop out. Convert them to real numbers. |
| Blank cells or logical values inside the range | Empty cells and TRUE/FALSE in a reference are not counted by these functions. |
| Zeros pull the CV down or up | Zero is a number; AVERAGE includes zeros. Remove placeholder zeros that are not real measurements. |
| #VALUE! or other error | An error value in an argument, or text typed directly into the argument list that cannot be converted to a number, makes the function return an error. |
| CV is huge or changes sign | The mean is near zero or negative. NIST notes the CV is unstable when the mean is near zero. |
Free alternatives
The CV is also a one-line calculation outside Excel. The rows below follow the CASRAI coefficient of variation guide.
| Tool | CV expression | Note |
|---|---|---|
| R | sd(x) / mean(x) * 100 |
Base R; sd() is the sample standard deviation. |
| Python (NumPy / pandas) | x.std() / x.mean() * 100 |
Use ddof=1 in np.std() for the sample standard deviation. |
| Python (SciPy) | scipy.stats.variation(x) |
Returns a proportion; multiply by 100 for a percentage. |
Frequently asked questions
How do I find the coefficient of variance in Excel?
Type =STDEV.S(range)/AVERAGE(range) and format the cell as a percentage. Use STDEV.P only if the range is the whole population.
How to calculate the coefficient of variability?
Coefficient of variability is another name for the same ratio: standard deviation divided by the mean, often multiplied by 100. The Excel steps above apply unchanged.
What are the formulas for standard deviation and variance?
In Excel, sample standard deviation is STDEV.S and population standard deviation is STDEV.P; sample variance is VAR.S and population variance is VAR.P. On the example data Microsoft’s pages give VAR.S = 754.27 and VAR.P = 678.84. Standard deviation is the square root of variance: the square root of 754.27 is 27.46, matching STDEV.S.
What are the formulas for calculating variance and coefficient of variation?
Variance: =VAR.S(A2:A11) (sample) or =VAR.P(A2:A11) (population). Coefficient of variation: =STDEV.S(A2:A11)/AVERAGE(A2:A11), or equivalently =SQRT(VAR.S(A2:A11))/AVERAGE(A2:A11).
How to calculate range in Excel?
Subtract the smallest value from the largest: =MAX(A2:A11)-MIN(A2:A11). For the example data that is 1370 – 1299 = 71. Range is a different measure of spread from the CV; for a more robust alternative see the interquartile range.
What is the difference between variance and variation?
Variance is a specific statistic: the average squared deviation from the mean, in squared units of the data. “Variation” is the general idea of spread, and the “coefficient of variation” is the unit-free ratio of standard deviation to mean. See standard deviation for how the two relate.
What does 20% variance mean?
If the 20% is a CV, it means the standard deviation is one fifth of the mean. There is no universal threshold that makes 20% good or bad; whether it is acceptable depends on the field and the measurement method. If someone means “20% difference between two figures” (for example budget variance), that is a different calculation, not a CV.
Sources
- Microsoft Support, STDEV.S function (checked 2026-10-29).
- Microsoft Support, STDEV.P function (checked 2026-10-29).
- Microsoft Support, AVERAGE function (checked 2026-10-29).
- Microsoft Support, VAR.S function and VAR.P function (checked 2026-10-29).
- NIST/SEMATECH Dataplot reference manual, Coefficient of Variation (checked 2026-10-29).
