Coefficient of Variation Calculator
Find relative spread from mean and standard deviation, for lab and survey data.
What it does
The coefficient of variation, often shortened to CV, turns absolute spread into relative spread. A standard deviation of 7.5 means little on its own. Paired with a mean of 50 it is 15 percent, but paired with a mean of 500 it is only 1.5 percent. CV puts those cases on the same scale.
The tool above divides your standard deviation by your mean and reports percent, ratio, and a plain band name. Enter the two numbers and read the three results. No units are needed because the units cancel in the division.
Analysts use CV to compare precision across instruments, batches, or surveys that live on different scales. A lab may accept under 10 percent for an assay, call 10 to 30 percent moderate, and flag above 30 percent for review. Finance, quality control, and field surveys use similar cutoffs, tuned to their own risk.
CV only fits ratio data with a true zero and a positive mean, such as counts, amounts, and concentrations. Do not use it for temperatures in Celsius or Fahrenheit, for Likert scores, or for means near zero, where a tiny shift in the mean swings CV wildly. In those cases report the standard deviation itself.
This page shows the formula, one full hand checked example at mean 50 with SD 7.5, a reference table of bands, and practice checks you can run through the tool.
How to use
- Find the mean of your data set from your software, spreadsheet AVERAGE, or a hand sum divided by n.
- Find the sample or population standard deviation in the same units as the mean.
- Type the mean in the Mean box. The default 50 matches the worked example.
- Type the standard deviation in the second box. The default 7.5 matches the worked example.
- Read CV percent as the main result, ratio as the decimal form, and band as Low, Moderate, or High spread.
- Rerun with a second data set to compare. The lower CV has tighter relative precision.
Formula
- mean
- Arithmetic average of the values, must be positive.
- SD
- Standard deviation in the same units as the mean.
- CV
- Relative spread in percent, unit free.
Use the same SD type throughout a comparison, either sample or population for all groups. If SD is 0, CV is 0 percent. If the mean is 0 or negative, the tool stops with an error because the ratio has no practical reading.
Worked example
Example: mean 50, SD 7.5
A batch assay has mean 50 units and standard deviation 7.5 units. Here is the full path to CV.
- Write the inputs: mean = 50, SD = 7.5.
- Divide: 7.5 / 50 = 0.15.
- Convert to percent: 0.15 x 100 = 15.0 %.
- Read the ratio output: 0.15 with no units.
- Read the band: 15.0 % sits in 10 to 30 %, so Moderate spread.
- Cross check: 15 % of 50 is 7.5, which returns the starting SD.
Reference table
| CV | Band | Usual reading |
|---|---|---|
| 0 to below 10 % | Low spread | Tight precision, often accepted |
| 10 to 30 % | Moderate spread | Usable, watch for drift |
| Above 30 % | High spread | Review method or sampling |
| SD = 0 | No spread | All values equal the mean |
Limits
- Needs a positive mean. Zero or negative means give no valid CV.
- Only fits ratio scales with a true zero, not interval scales like Celsius.
- Unstable when the mean is near zero, where small mean shifts swing CV.
- Does not show skew or outliers. Pair it with a plot for strange data.
Common mistakes
- Dividing by a mean near zero and trusting the huge percent that results.
- Mixing sample SD for one group with population SD for another in the same comparison.
- Using CV on Fahrenheit or Celsius temperatures, where zero is not true zero.
- Forgetting to multiply by 100, so 0.15 is reported as 0.15 percent instead of 15.0 percent.
- Comparing CVs from different units without checking that each SD matches its own mean.
Try it yourself
Quick checks. Answers sit tucked under each question.
CV for mean 100 and SD 5?
5 / 100 = 0.05, times 100 = 5.0 %. Band Low spread.
CV for mean 200 and SD 60?
60 / 200 = 0.3, times 100 = 30.0 %. Band Moderate spread.
Questions
What is coefficient of variation?
SD divided by mean, times 100. It reports spread as percent of the mean.
What is a good CV?
Many labs aim below 10 %. 10 to 30 % is often usable. Above 30 % usually triggers review. Targets vary by field.
Can CV be over 100 %?
Yes, when SD exceeds the mean. That signals very high relative spread.
CV or standard deviation?
Use SD for one scale in original units. Use CV to compare groups on different scales.
Why does my CV fail with mean 0?
Division by zero has no finite answer. Report SD alone when the mean is zero.
Sample or population SD?
Either, if you stay consistent. Mixing the two across groups biases the comparison.