Coefficient of Variation Calculator
Relative variability — the standard deviation as a percentage of the mean, which lets you compare the spread of things measured on different scales.
CV = σ ÷ μ, usually quoted as a percentage.
How the coefficient of variation calculator works
CV = σ ÷ μ, usually quoted as a percentage. Because both parts carry the same units, they cancel: the result is dimensionless, so a CV of 15% means the same thing whether you are measuring dollars, kilograms or milliseconds.
It only makes sense on a ratio scale with a meaningful zero and a positive mean. Applied to temperatures in Celsius it produces nonsense, because the zero is arbitrary.
Formula: CV = σ / μ × 100%
Worked examples
| Inputs | Coefficient of variation (sample) | Note |
|---|---|---|
| Five values near 50 | 7.6158% | CV ≈ 7.7% |
| Identical values | 0% | CV = 0 |
| Highly variable | 147.9591% | CV ≈ 150% |
FAQFrequently asked questions
What is a good coefficient of variation?
It depends entirely on the field. Under 10% is tight for most measurements; laboratory assays often demand under 5%; biological and financial data routinely exceed 30%.
Why not just use the standard deviation?
Because it carries units. A SD of 5 kg means something very different for infants and for elephants; the CV makes them comparable.
When does it break?
When the mean is near zero — the ratio explodes — or when the zero point is arbitrary, like Celsius. Use it only on ratio scales.
Is it the same as relative standard deviation?
Yes. RSD is the same quantity, usually quoted as a percentage in analytical chemistry.
What is the signal-to-noise ratio?
Simply the reciprocal: mean ÷ SD. Engineers prefer it because larger is better.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.