Coefficient of Variation Calculator
The coefficient of variation is the standard deviation divided by the mean, shown as a percentage: CV = (SD ÷ mean) × 100. Enter your data to get the CV with the mean, standard deviation, and every step.
Coefficient of variation (CV) is your standard deviation divided by your mean, written as a percentage: CV = (SD ÷ mean) × 100. Plug in your numbers above and you get the CV plus the mean, standard deviation, variance, and every step behind it. A data set with a mean of 50 and a standard deviation of 5 has a CV of 10%, meaning the values sit about 10% away from their own average.
The real value of CV is comparison. Because it strips out units, you can line up a data set measured in dollars against one measured in kilograms and still say which is more consistent. That is something a plain standard deviation can never tell you.
What is the coefficient of variation?
The coefficient of variation measures how spread out a data set is relative to its own average. You take the standard deviation, divide it by the mean, and multiply by 100 to get a percentage. A small CV means the numbers cluster tightly around the mean. A large CV means they scatter far from it.
Think of two classes that both average 70 on a test. One class scores between 68 and 72. The other scores between 40 and 100. Same mean, wildly different consistency. The coefficient of variation catches that difference in a single number, where the raw standard deviation alone can be misleading when averages differ.
What is the coefficient of variation formula?
The formula is short:
CV = (Standard Deviation ÷ Mean) × 100
Written with symbols, a sample uses CV = (s ÷ x̄) × 100 and a population uses CV = (σ ÷ μ) × 100. The only moving parts are the standard deviation on top and the mean on the bottom. Multiply by 100 and you have a percentage. Skip the ×100 and you have the CV as a plain ratio, which some textbooks prefer.
Sample formula vs population formula
The formula splits based on whether your data is a sample or a full population, and the split happens inside the standard deviation.
| Data type | Formula | SD divides by | When to use it |
|---|---|---|---|
| Sample | CV = (s ÷ x̄) × 100 | n − 1 | You measured part of a larger group (most coursework and research) |
| Population | CV = (σ ÷ μ) × 100 | N | You have every value in the whole group |
Pick sample unless you genuinely have data for the entire population. Dividing by n − 1 gives a slightly larger standard deviation, so the sample CV always comes out a little higher than the population CV on the same numbers. For the set 10, 34, 23, 54, 9, the sample CV is 72.01% and the population CV is 64.40%.
How do you calculate the coefficient of variation step by step?
You need two things: the mean and the standard deviation. Here is the full process on a small data set so you can follow every number.
Data set: 2, 4, 6, 8, 10 (treated as a sample)
- Find the mean. Add the values and divide by the count. (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6.
- Find each squared deviation. Subtract the mean from every value, then square it: (−4)² = 16, (−2)² = 4, 0² = 0, 2² = 4, 4² = 16. These add up to 40.
- Find the standard deviation. Divide the total by n − 1, then take the square root: √(40 ÷ 4) = √10 = 3.1623.
- Divide by the mean and multiply by 100. (3.1623 ÷ 6) × 100 = 52.7%.
So the coefficient of variation is 52.7%. The standard deviation is about 53% of the mean, which is high, so this data is quite spread out relative to its average. You can check any of these middle steps with the mean calculator or the variance calculator.
How do you calculate coefficient of variation from standard deviation and mean?
If you already have the standard deviation and the mean, you skip straight to the last step. Divide the standard deviation by the mean and multiply by 100. That is it.
Say a lab reports a mean of 50 and a standard deviation of 5. CV = (5 ÷ 50) × 100 = 10%. Or a mean of 120 with a standard deviation of 18: CV = (18 ÷ 120) × 100 = 15%. No raw data needed once you have those two numbers.
What does standard deviation divided by the mean tell you?
Standard deviation divided by the mean is the coefficient of variation as a ratio. Multiply that ratio by 100 and you get the more common percentage form. So “standard deviation over mean” and “coefficient of variation” describe the same calculation, just before or after the ×100 step.
The reason this ratio matters: a standard deviation of 5 is tiny next to a mean of 1000 but enormous next to a mean of 8. Dividing by the mean puts the spread in context, which is exactly why CV works for comparing data on different scales. If you plot both sets, how spread shows up on a bell curve makes the same point visually.
How do you find percent CV (%CV)?
Percent CV, written %CV, is just the coefficient of variation expressed as a percentage. There is no separate calculation. When you multiply the standard-deviation-to-mean ratio by 100, the result is your %CV. A ratio of 0.25 becomes a %CV of 25%.
Labs and analytical chemistry lean on %CV to describe how repeatable a measurement is. A %CV under 5% usually signals a precise, reliable assay, while a %CV climbing past 15% often flags a method that needs tightening.
How do you calculate coefficient of variation in Excel?
Excel has no single CV function, so you combine two functions. If your numbers sit in cells A1 through A10:
- For the ratio:
=STDEV.S(A1:A10)/AVERAGE(A1:A10) - For the percentage:
=(STDEV.S(A1:A10)/AVERAGE(A1:A10))*100
Use STDEV.S when your data is a sample, which covers almost every real case. Switch to STDEV.P only when the cells hold an entire population. Mixing these up is the most common Excel error with CV, and it quietly makes your sample result slightly larger than the population result every time. The size of that gap is fixed and predictable: it depends only on how many values you have, never on the values themselves. Google Sheets uses the exact same functions, so the formulas carry over unchanged.
What is a good coefficient of variation?
There is no fixed cutoff, but a few bands show up again and again across fields. The table below gives the rough ranges most analysts work with.
| CV range | Interpretation | Typical setting |
|---|---|---|
| Below 15% | Low variation, consistent and predictable | Lab measurements, quality control |
| 15% to 30% | Moderate variation, normal for many real data sets | Survey data, business metrics |
| Above 30% | High variation, inconsistent or volatile | Speculative investments, unstable processes |
What counts as “good” depends entirely on your field. A stock with a CV of 40% is not automatically bad, it just carries more volatility per unit of return than one at 20%. On a factory line, a CV above 10% might already be a red flag. Always judge the number against your own benchmark, not a universal rule.
Why compare data sets with the coefficient of variation?
This is where CV earns its keep. Because it has no units, it lets you compare spread across data sets that would otherwise be impossible to line up.
Take two investments. Stock A returns 8, 10, 12, 9, 11 (percent) over five periods. Stock B returns 5, 15, 25, 10, 20. Both look active, but which is steadier relative to its own average?
| Data set | Mean | Sample SD | CV |
|---|---|---|---|
| Stock A: 8, 10, 12, 9, 11 | 10 | 1.5811 | 15.81% |
| Stock B: 5, 15, 25, 10, 20 | 15 | 7.9057 | 52.70% |
Stock A has the lower CV, so its returns are far more consistent relative to its average. Stock B swings much harder. A plain standard deviation would have hinted at this, but the CV makes the gap unmistakable and scale-proof.
When should you not use the coefficient of variation?
CV has one hard limit: it only works for data measured on a ratio scale with a positive mean. That means data where zero means “none” and values cannot go negative, like weights, prices, distances, and counts.
It breaks down for temperature in Celsius or Fahrenheit, because zero on those scales is arbitrary, not a true “none.” It also fails when the mean is zero (you would be dividing by zero) or negative (the result loses meaning). If your data can dip below zero or sits on an interval scale, reach for the standard deviation instead.
Worked examples of the coefficient of variation
Here are several data sets run through the full formula so you can match your own homework against a verified answer. All use the sample formula (dividing by n − 1).
| Data set | Mean | Sample SD | CV (%) |
|---|---|---|---|
| 10, 34, 23, 54, 9 | 26 | 18.7216 | 72.01% |
| 2, 4, 6, 8, 10 | 6 | 3.1623 | 52.70% |
| 98, 99, 100, 101, 102 | 100 | 1.5811 | 1.58% |
| 8, 10, 12, 9, 11 | 10 | 1.5811 | 15.81% |
Notice the last two rows. Both have the same standard deviation of 1.5811, but very different CVs (1.58% versus 15.81%) because their means differ by a factor of ten. That is the coefficient of variation doing its job: scaling the spread to the size of the numbers.
Frequently asked questions
How do you calculate the coefficient of variation?
Divide the standard deviation by the mean, then multiply by 100. The result is the coefficient of variation as a percentage. For example, a standard deviation of 5 and a mean of 50 give a CV of 10%.
How do you calculate the coefficient of variation from the standard deviation?
If you already know the standard deviation and the mean, divide the standard deviation by the mean and multiply by 100. You do not need the raw data again once you have those two numbers.
Is the coefficient of variation the same as standard deviation divided by the mean?
Yes. Standard deviation divided by the mean is the coefficient of variation as a ratio. Multiplying that ratio by 100 turns it into the percentage form most people quote.
What is a good %CV value?
It depends on the field. A %CV below 15% usually signals consistent data, and labs often want it under 5%. Values above 30% point to high variability. Compare your %CV to the standard in your own area rather than a fixed cutoff.