What Is Coefficient of Variation?
The coefficient of variation is the standard deviation divided by the mean, usually written as a percentage. Because it has no units, it lets you compare the relative variability of data sets measured on different scales.
Many people search for "coefficient of variance"; the standard term is coefficient of variation, and the two refer to the same calculation here. The calculator also returns the CV as a ratio, a bias-corrected CV for small samples and the range mean ± SD. It works best for ratio-scale data with a positive mean.
Below you will find the formulas, a variables table, a worked example and answers to common questions such as CV versus RSD and when the CV is misleading.
How to Use the Coefficient of Variation Calculator
- Choose raw data or mean and SD.
- For raw data, pick sample or population.
- Read the CV as a percentage. Lower means more consistent relative to the mean.
- Compare it with the CV of another data set, not with the raw standard deviations.
Coefficient of Variation Formula
Coefficient of variation
Small-sample correction
Coefficient of Variation Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| CV | Coefficient of variation | s ÷ |x̄|, shown as % |
| s | Standard deviation | |
| x̄ | Mean | Should be well away from zero |
| n | Number of values | Needs at least 2 for raw data |
Coefficient of Variation Worked Example
Using the example values (press “Load example” above to try them):
- Standard deviation = 2.16025 and mean = 22.
- CV = SD ÷ |mean| = 2.16025 ÷ 22 = 0.098193.
- As a percentage: 0.098193 × 100 = 9.8193 %.
Result: Coefficient of variation (CV) = 9.8193 %; CV as a ratio = 0.098193.
How to interpret a CV
There is no universal cut-off for a “good” CV, because it depends on the field and the measurement. The bands below are common rules of thumb for general data; laboratories, manufacturers and financial analysts each use their own thresholds.
| CV | Reading | Example context |
|---|---|---|
| Below 10% | Very low variability | Precise instrument replicates |
| 10% to 20% | Low | Consistent process output |
| 20% to 35% | Moderate | Biological measurements |
| 35% to 70% | High | Daily sales, rainfall in a region |
| Above 70% | Very high | Highly skewed or volatile data |
When not to use the CV
- Interval-scale data with an arbitrary zero (temperature in °C or °F). A shift in the zero changes the CV.
- Data with a mean near zero, where the ratio explodes and is unstable.
- Data that take both positive and negative values, where the mean no longer reflects size.
- Very small samples, where both the mean and SD are noisy.
CV, RSD and standard deviation compared
CV and RSD are the same quantity in different clothes: ratio versus percent. Analytical chemistry usually says RSD; statistics and finance usually say CV.
| Measure | Formula | Units |
|---|---|---|
| Standard deviation | s | Same as data |
| Coefficient of variation | s / |x̄| | None (ratio) |
| Relative standard deviation | 100 × s / |x̄| | Percent |
| Standard error | s / √n | Same as data |
Where Coefficient of Variation Is Used
Comparing variability across scales
Judging which data set is relatively more variable.
Lab precision
Reporting repeatability as a percentage.
Finance and operations
Comparing spread relative to the average level.
Coursework
Checking CV calculations from raw data or summary values.
Common Coefficient of Variation Mistakes to Avoid
- Use CV to compare variability, not to describe a single data set on its own.
- Check that zero genuinely means “none” on your scale before using a CV.
- For small samples consider the bias-corrected figure.
Coefficient of Variation Terms and Definitions
- Ratio scale
- A scale with a true zero where ratios are meaningful (weight, length, money).
Coefficient of Variation FAQs
What is the coefficient of variation?
It is the standard deviation divided by the mean, often expressed as a percentage. It measures relative variability.
What is a good coefficient of variation?
It depends on the field. Lower values mean more consistent data relative to the mean; compare against norms for your own measurement or industry.
Is CV the same as RSD?
Yes. RSD is just the CV multiplied by 100 and reported as a percentage.
Can the coefficient of variation be over 100%?
Yes. It happens when the standard deviation is larger than the mean, typical of strongly skewed data.
Why can’t I use CV for temperature in Celsius?
Celsius has an arbitrary zero. Changing to Kelvin changes the mean and therefore the CV, so the ratio is not meaningful.
Should I use sample or population SD?
Use the sample SD (n − 1) for samples, which is the usual case.