What this calculator does
See how spread out your numbers are compared with their average, as one easy percentage. This is the coefficient of variation (CV), also called the relative standard deviation (RSD). A standard deviation of 5 is large for values around 10 but tiny for values around 1,000. Dividing by the mean (the average) puts both on the same footing. The result has no units and is usually shown as a percentage.
Paste your data and choose whether it is a sample or a whole population. The calculator then finds the mean, the matching standard deviation and the CV, with each step shown.
Where it's used
Why this math matters outside the classroom:
- Comparing funds. A fund averaging 8% a year with SD 4% has a CV of 50%, lower than one averaging 12% with SD 9%, whose CV is 75%.
- Lab precision. A lab whose repeat measurements of one sample average 100 with SD 3 reports a CV of 3% to describe its precision.
- Filling lines. A line filling 500 mL bottles with SD 5 mL has a CV of 1%, while a 50 mL line with SD 2 mL has a CV of 4%.
- Different units. Researchers compare the spread of heights in cm and weights in kg with the CV, since it has no units.
- Crop yields. Fields with mean yields of 150 and 180 bushels per acre and SDs of 15 and 27 have CVs of 10% and 15%.
How to use it
- Enter or paste at least two numbers, separated by commas, spaces or new lines.
- Choose Sample if the data is a subset of a larger group, or Whole population if it includes every member.
- Read the CV as a percentage. The ratio form, the standard deviation and the mean are listed below it.
What the inputs mean
- Data set
- CV is meant for data measured on a scale with a true zero, such as weights, times, concentrations or prices. It is not meaningful for temperatures in °C or °F or for data that mixes positive and negative values.
- Your data is a
- The sample version uses the standard deviation that divides by n − 1; the population version divides by n. The sample CV is slightly larger.
Formula and method
CV = s ÷ x̄ × 100% (sample) CV = σ ÷ μ × 100% (population)
In the formulas, s is the sample standard deviation and x̄ ("x-bar") is the sample mean. For a whole population, σ (sigma) is the standard deviation and μ (mu) is the mean.
First the calculator finds the mean. Next it squares how far each value sits from the mean and adds those up. It divides that sum by n − 1 for a sample or by n for a population, where n is the count of values. The square root of that is the standard deviation. The CV is that standard deviation divided by the mean.
Because the units cancel, you can compare CVs across data sets measured in different units or on very different scales. If the mean is zero, the ratio is undefined, so the calculator shows an error instead of a result.
Worked example
A sample of eight measurements: 2, 4, 4, 4, 5, 5, 7 and 9.
- Mean: 40 ÷ 8 = 5.
- Sum of squared deviations from 5: 32. Sample standard deviation: √(32 ÷ 7) ≈ 2.1381.
- CV = 2.1381 ÷ 5 × 100 ≈ 42.7618%.
- Treated as a population instead, σ = √(32 ÷ 8) = 2 and CV = 2 ÷ 5 × 100 = 40%.
Result: The sample coefficient of variation is about 42.7618% (40% as a population).
Understanding the result
A lower CV means more consistent data relative to its size. In lab and manufacturing settings, repeated measurements are often judged by how small their RSD is, with acceptable limits set by the method or industry.
Use CV to compare variability across groups with different means, such as the consistency of two machines producing parts of different sizes. When the means are similar, comparing standard deviations directly works just as well.
A CV above 100% means the standard deviation is larger than the mean, which usually signals highly skewed data or values close to zero.
Assumptions and limitations
- All values are on a ratio scale with a meaningful zero, and the mean is positive.
- Every value counts equally. The standard deviation is computed with a two-pass method for accuracy.
- When the mean is close to zero, the CV becomes very large and unstable, and small changes in the data swing it widely.
- If the mean is negative, the CV is negative; this calculator reports it with a note, but such a CV is rarely meaningful.
- The CV of a small sample is a rough estimate. At most 10,000 values are accepted.
Frequently asked questions
Is the coefficient of variation the same as relative standard deviation?
Yes. Relative standard deviation (RSD), often written %RSD, is the same quantity: the standard deviation divided by the mean, usually as a percentage. Some fields report it as a plain ratio instead.
What is a good coefficient of variation?
It depends entirely on the field and what is being measured. Precise lab assays may aim for a few percent, while biological or financial data can have CVs well above 30%. Compare against the norms for your measurement rather than a universal cutoff.
Why can't I use CV for temperatures in Celsius?
Zero degrees Celsius is not a true absence of temperature, so dividing by the mean gives a number that changes if you switch to Fahrenheit. CV only makes sense when zero means none of the quantity, as with Kelvin, weight or time.
Should I use the sample or population version?
Use the sample version when your data is a subset used to describe a larger group, which is the usual case. Use the population version only when the data covers every member of the group.
How this calculator is checked
Method: Coefficient of variation CV = SD/mean (Pearson), using the sample (n − 1) or population (n) standard deviation. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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