Coefficient of Variation Calculator
What the coefficient of variation (CV) tells you
The coefficient of variation (CV) is a unitless measure of relative dispersion. It expresses how large the standard deviation is compared with the mean, which makes it useful when you want to compare variability across datasets that have different units or very different magnitudes (for example, returns in % vs. thickness in mm). Because it is scaled by the mean, CV answers a different question than standard deviation: not “how spread out are the values?” but “how spread out are they relative to their average?”
CV is commonly reported as a percentage. A larger CV indicates more variability relative to the mean; a smaller CV indicates tighter clustering around the mean. Interpretation is domain-specific—what is “high” in one field may be normal in another—so CV is best used for comparisons (dataset A vs. dataset B) rather than universal thresholds.
Formulas used (sample vs. population)
This calculator uses the sample standard deviation by default, which is typical when you input observed data rather than an entire population. The key quantities are:
- Mean:
- Sample standard deviation:
- Coefficient of variation (percent):
MathML (sample CV, expressed as a percentage):
If you truly have population data, you would use the population standard deviation instead of . The CV structure is the same: (times 100 for percent).
How to use the calculator
- Enter your values separated by commas or spaces (e.g.,
4.9, 5.1, 5.0). - Click Calculate.
- Review the mean, standard deviation, and CV. Use the CV to compare relative variability between datasets.
Interpreting the results
CV is unitless. If your data is measured in dollars, millimeters, or seconds, the CV does not carry those units—only the relative spread remains. Practical interpretation often looks like:
- Lower CV → more consistency relative to the mean (less relative variability).
- Higher CV → less consistency relative to the mean (more relative variability).
CV is especially informative when comparing two processes or portfolios with different averages. A dataset can have a larger standard deviation but a smaller CV if its mean is much larger.
Worked example
Suppose you measure the thickness of 10 metal plates (mm):
4.9, 5.1, 5.0, 4.8, 5.2, 5.1, 4.9, 5.0, 5.2, 5.1
- Mean ≈ 5.02
- Sample standard deviation ≈ 0.14
- CV% = (0.14 / 5.02) × 100 ≈ 2.8%
A CV around 2.8% indicates the thickness measurements are very consistent relative to their average.
Comparison table: standard deviation vs. coefficient of variation
| Metric | What it measures | Units | Best for | Common pitfalls |
|---|---|---|---|---|
| Standard deviation (s or σ) | Absolute spread around the mean | Same as the data | Variability within one scale/unit | Hard to compare across different magnitudes/units |
| Coefficient of variation (CV) | Relative spread scaled by the mean | Unitless (often %) | Comparing variability across datasets | Unstable/undefined when mean is near or equal to 0 |
Assumptions & limitations
- Mean must be non-zero: CV is undefined when the mean equals 0 because it divides by the mean.
- Near-zero means can be misleading: when the mean is very small, CV can become extremely large and unstable (small rounding or noise changes the ratio a lot).
- Negative values: if the mean is negative, the raw formula yields a negative CV. In many disciplines CV is reported as a non-negative magnitude; consider using |mean| in the denominator if that matches your domain conventions, and be explicit about the choice.
- Sample vs. population: this calculator uses sample standard deviation (n−1). If you need a population CV, use σ with denominator n.
- Input cleaning: results depend on valid numeric inputs. Empty entries or non-numeric tokens should be ignored or flagged by the calculator implementation.
- Rounding: displayed results may be rounded for readability; small discrepancies vs. spreadsheet software can occur due to rounding/precision differences.
FAQ
Is the coefficient of variation unitless?
Yes. CV is a ratio of two quantities with the same units (standard deviation and mean), so units cancel out. It is often reported as a percentage.
When is CV not appropriate?
CV is not appropriate when the mean is 0 (undefined) and can be unreliable when the mean is close to 0. It can also be less meaningful for data that naturally spans positive and negative values where the mean can be near zero.
Why use sample standard deviation instead of population standard deviation?
When your input values are a sample from a larger process, the sample standard deviation (using n−1) provides an unbiased estimate of population variability. If you have the entire population, the population standard deviation (using n) may be more appropriate.
Can the coefficient of variation be negative?
It can be negative if you compute CV% = (s / mean) × 100 and the mean is negative. Many references report CV as non-negative; check your field’s convention and consider whether to use the absolute value of the mean.