# What is the coefficient of variation?

Computes the coefficient of variation (CV) of a list of numbers, the sample or population standard deviation divided by the mean, as a percent and a ratio.

- Page: https://www.acalculator.org/statistics/coefficient-of-variation-calculator
- JSON spec: https://www.acalculator.org/statistics/coefficient-of-variation-calculator.json
- Version: 5e30e6c3e761

## Default answer

Example with the default inputs (Data values [10, 12, 23, 23, 16, 23, 21, 16], Data are a Sample (n − 1)): The coefficient of variation of the 8 values is 29.0957%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| x | Data values | The numbers, separated by commas, spaces, semicolons, or new lines. |
| type | Data are a | Sample: the standard deviation divides by n − 1. Population: every member is listed, so it divides by N. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| percent | Coefficient of variation (CV) | The standard deviation as a percent of the mean: 100 × s ÷ x̄ (negative when the mean is). |
| rsd | Relative standard deviation (RSD) | The standard deviation as a percent of the size of the mean: 100 × s ÷ \|x̄\|. |
| cv | CV as a ratio | s ÷ x̄, not multiplied by 100. |
| mean | Mean (x̄) | The sum of the values divided by their count. |
| sd | Standard deviation (s) | The sample (n − 1) or population (N) standard deviation, as chosen. |
| n | Count (n) | How many values there are. |

## Method

CV = s ÷ x̄, shown as 100 × s ÷ x̄ percent; s is the sample (n − 1) or population (N) standard deviation.

## Assumptions

- The CV is meaningful for data on a ratio scale (a true zero), such as lengths, weights or times.
- The CV is not defined when the mean is 0; near 0 it changes a lot with small changes in the data.
- A negative mean gives a negative CV; the relative standard deviation uses the size of the mean instead.

## Worked examples

1. x = 10 or 12, type = sample gives percent = 29.095719%, rsd = 29.095719%, cv = 0.290957, mean = 18, sd = 5.237229, n = 8. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02); NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (s² = Σ(Y − Ȳ)² ÷ (N − 1)), https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm (retrieved 2026-10-02).
2. x = 2 or 4, type = population gives percent = 40%, cv = 0.4, mean = 5, sd = 2. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02).
3. x = -4 or -6, type = sample gives percent = -33.333333%, rsd = 33.333333%, mean = -6, sd = 2. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02).

## FAQ

### What is the coefficient of variation?

The standard deviation divided by the mean, cv = s ÷ x̄. It measures spread relative to the size of the values, so it has no unit. It is often written as a percent: 100 × s ÷ x̄.

### How do I calculate the coefficient of variation?

Find the mean, find the standard deviation, and divide. For 10, 12, 23, 23, 16, 23, 21, 16: the mean is 18, the sample standard deviation is 5.2372, and 5.2372 ÷ 18 = 0.29096, or 29.10%.

### What is a good coefficient of variation?

There is no single cut-off; it depends on the field. A lower CV means the values sit closer to their mean. Laboratories often set their own limits for repeat measurements, such as a few percent, while biological or sales data can have CVs far above 30%.

### Is the coefficient of variation the same as the relative standard deviation?

Nearly. NIST defines the relative standard deviation as 100 × s ÷ |x̄|, the CV as a percent but with the size of the mean. They differ only when the mean is negative, where the CV is negative and the RSD is not.

### Should I use the sample or the population standard deviation?

Use the sample one (dividing by n − 1) when your numbers are a sample from a larger group, which is the usual case. Use the population one (dividing by N) only when you have every member of the group.

### Why can the CV not be used when the mean is 0?

Dividing by 0 is not defined, and near 0 a tiny change in the mean makes the CV jump. That is why NIST says the CV suits data on a ratio scale, with a true zero and positive values, such as weights or times, and not temperatures in °C.

## Sources

- NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (the sample coefficient of variation is the ratio of the standard deviation to the mean, cv = s ÷ x̄; used for data on a ratio scale; the relative standard deviation is 100 s ÷ |x̄|). https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02)
- NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (sample variance and standard deviation with N − 1). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm (retrieved 2026-10-02)