Coefficient of Variation Calculator
What the coefficient of variation shows
Two datasets can share an identical mean while one swings wildly and the other barely moves. The coefficient of variation (CV) captures that spread relative to the average: CV = SD / mean * 100. Because the units cancel, a 4 cm standard deviation on 50 cm and a 4 kg one on 50 kg both read 8 percent.
Ops teams gauge process consistency, finance desks compare volatility across assets, and labs compare assay precision with this single unit-free number. It is the standard yardstick for asking which line, fund, or assay is relatively noisier.
Computing CV, with numbers
The formula needs two summaries: CV = (SD / mean) * 100. A filling line with a sample mean of 500 mL and a standard deviation of 12 mL scores CV = 12 / 500 * 100 = 2.4 percent, while a machine averaging 250 mL with the same SD returns 4.8 percent, twice as noisy in relative terms.
Use the sample standard deviation, with n minus 1 in the denominator, whenever the data are a sample rather than the whole population.
Running the calculator
Decide what to Calculate from: Summary Data, if you already know the Standard deviation and Sample mean, or Raw Data, if you will paste observations for the tool to process.
Specify whether the Data for is proportions or means, note the Sample size and how to Input outcome as, then press Calculate. Compare CVs only within similar measurement types, because 2 percent on revenue and 2 percent on part diameters carry very different practical weight.
Frequently Asked Questions
What does the coefficient of variation measure?
It measures relative dispersion: the standard deviation expressed as a percentage of the mean. CV = SD / mean * 100, so 12 mL of spread around 500 mL equals 2.4 percent.
When is CV more useful than SD?
Whenever you compare variability across different scales or units. A 10 minute SD means little alone, but against a 15 minute mean it reveals 67 percent relative noise and serious inconsistency.
Can a CV be negative or above 100?
The standard CV makes sense only for positive means, so it suits quantities like sales or concentrations. A value above 100 percent simply means the SD exceeds the mean, signaling severe instability.
Summary data or raw data entry?
Choose Summary Data when a report already lists the standard deviation and sample mean, and Raw Data when you have the individual observations. The tool computes the same CV either way.
How does sample size affect the CV?
CV is a point summary, but its reliability improves with n. From raw data, the tool uses the Sample size to build the mean and SD, so small samples yield noisier CVs.