Coefficient of Variation Calculator
Calculate the coefficient of variation (CV) — standard deviation as a percentage of the mean.
How to use this tool
- Enter mean (μ or x̄) and standard deviation (σ or s) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your coefficient of variation (%) and the full breakdown beneath it.
CV = (SD / |mean|) × 100. Expresses variability relative to the mean, making datasets with different units comparable.
Formula
CV (%) = (σ / |μ|) × 100
Where σ (or s) is the standard deviation and μ (or x̄) is the mean. The absolute value of the mean is used so that CV is always non-negative.
How it works
The coefficient of variation expresses the standard deviation as a percentage of the mean, allowing the relative variability of datasets with different units or scales to be compared directly.
This calculator requires the mean and standard deviation to be entered directly. It is most meaningful when the mean is positive and the data are measured on a ratio scale; CV is undefined when the mean is zero and can be misleading for data that includes negative values.
Worked example
Worked example
- Inputs: mean μ = 50, standard deviation σ = 10.
- Divide: σ / |μ| = 10 / 50 = 0.20.
- Convert to percentage: 0.20 × 100 = 20.0%.
Coefficient of variation CV = 20.0%
Key terms
- Coefficient of variation (CV)
- A dimensionless ratio of the standard deviation to the mean, expressed as a percentage; measures relative dispersion independently of the unit of measurement.
- Standard deviation (σ or s)
- The square root of the variance; measures the average spread of individual values around the mean.
- Relative variability
- The degree of spread in a dataset expressed in proportion to its mean, enabling comparison across datasets with different scales or units.
- Ratio scale
- A measurement scale with a true zero point (e.g., mass, length, time), for which CV is meaningful. CV should not be used for interval scales like temperature in Celsius.
- Risk and quality applications
- CV is widely used in finance (comparing asset volatility), analytical chemistry (assessing measurement precision), and manufacturing quality control.
Frequently asked questions
- When is CV useful?
- CV is useful when comparing variability between datasets with different means or units. A CV of 20% means the standard deviation is 20% of the mean. Lower CV indicates more consistency.