How do I calculate the coefficient of variation?

Divide the standard deviation by the mean and multiply by 100. For 10.1, 9.8, 10.3, 10, 9.9 the mean is 10.02 and the sample SD is 0.1924, so CV = 0.1924 / 10.02 × 100 = 1.92%. If you only have a mean and an SD, use the Mean and SD tab.

Is %RSD the same as CV?

Yes. Relative standard deviation (RSD) and coefficient of variation are the same quantity, SD divided by the mean. Analytical chemistry usually says %RSD and biology and statistics usually say %CV. The ICH M10 glossary defines precision as the CV or RSD expressed as a percentage.

Should I use sample or population standard deviation?

Use the sample SD (n − 1) for replicate measurements, which is what most labs and software report. Use the population SD (n) only when your data are the entire group of interest. The calculator shows both CVs and lets you pick which one drives the headline number, the chart and the report sentence.

What is an acceptable CV for an assay?

It depends on the method and your SOP. For bioanalytical method validation, the FDA 2018 guidance and ICH M10 say precision should not exceed 15% CV for chromatographic assays (20% at the LLOQ) and 20% CV for ligand-binding assays such as ELISA (25% at the LLOQ and ULOQ). Many labs set tighter in-house limits for routine runs. This page does not state any other threshold, so use the limit written in your own protocol.

Can the CV be over 100%?

Yes. It happens when the SD is larger than the mean, which is common for skewed data or means near zero. A CV that high usually says the CV is the wrong summary for those data, so look at the distribution or use another measure of spread.

How was the calculator checked?

For 30 random data sets with 2 to 25 values each, the mean, both SDs and both CVs were compared with NumPy and SciPy (scipy.stats.variation with ddof=0 and ddof=1) and agreed to better than one part in 10^12. The precision limits were read from the FDA 2018 guidance and the ICH M10 text. Those checks cover the cases tried, not every possible input.

Coefficient of Variation Calculator

Find the CV and %RSD from pasted replicates or a mean and SD, compare groups, and check against FDA and ICH M10 precision limits. Free, no sign-up.

Paste replicates or enter a mean and SDSample and population SD, CV and %RSDCompare up to 5 groupsDot plot with SD bands, PNG and SVG

Plot readings in run order on a control chart with a center line and control limits.Open

Standard deviation used for the CV

Sample SD is the default and fits replicates drawn from a larger process. Both CVs are always listed in the table.

Repeated measurements (commas, spaces or new lines)

Check the CV against a precision limit (optional)

These are precision limits for method validation accuracy and precision runs. For routine batches, follow your SOP.

CV = %RSD (sample SD)

1.92%

Mean

10.02

SD (n − 1)

0.1924

Mean ± SD

10.02 ± 0.1924

CV (population SD)

1.72%

Report sentence

Replicate measurements (n = 5) had a mean of 10.02 and a sample standard deviation of 0.1924, giving a coefficient of variation (CV) of 1.92%.

Excel and Google Sheets

=STDEV.S(A1:A10)/AVERAGE(A1:A10)

Format the cell as a percentage. Replace A1:A10 with your range.

Free Coefficient of Variation Charts

Every chart below is drawn from the same code as the calculator above. View and download them free, no sign-up.

One group

Replicate Dot Plot with SD Bands

Five readings, mean 10.02, sample SD 0.1924, CV 1.92%. Four of the five points sit inside one SD of the mean.

1 / 6

Charts

How it works

Reference

What the coefficient of variation is

The coefficient of variation (CV) is the standard deviation divided by the mean, usually written as a percentage. It tells you how large the scatter is compared with the size of the measurement. In analytical chemistry and biology the same number is called the relative standard deviation (RSD), and %RSD and %CV mean the same thing. Because the units cancel, you can compare the repeatability of a balance reading in grams with a pipetting result in microlitres, or a method run at 5 ng/mL with one run at 500 ng/mL.

Formula, sample SD and population SD

CV = SD / mean, and %CV = 100 × SD / mean. The only choice is which SD to use.
The sample SD divides the squared deviations by n − 1. It is the usual choice for repeated measurements, which are a small sample from everything the method could produce, and it is the default here. The population SD divides by n and fits the case where your data are the whole group, such as every unit in a small batch. The two CVs differ by a factor of sqrt(n / (n − 1)), which is 1.118 at n = 5 and 1.017 at n = 30. For the example data (10.1, 9.8, 10.3, 10, 9.9) the sample CV is 1.92% and the population CV is 1.72%.

When not to use the CV

The CV is meant for ratio-scale data, where zero means none of the quantity: mass, concentration, length, counts, time. It is misleading for interval scales such as temperature in Celsius or Fahrenheit, because moving the zero point changes the mean and so the CV.
It also breaks down when the mean is close to zero, because a tiny mean inflates the ratio, and it is undefined when the mean is zero. Data with negative values rarely suit it. The calculator warns you in each of these cases.
Finally, a CV from three or four replicates is a rough estimate. Treat small differences between two CVs as noise unless you have more data.

CV versus standard deviation

The SD is in the units of the data, so it cannot be compared across different scales. The CV can. Take two samples: Sample A has a mean of 10 and an SD of 1, so its CV is 10.00%; Sample B has a mean of 100 and an SD of 5, so its CV is 5.00%. Sample B has five times the SD but half the relative spread. If you want to describe where a single value sits relative to the mean in SD units instead, that is a z-score.

Precision limits in bioanalytical method validation

The calculator can compare a CV with the precision limits in two regulatory documents. We read the limits from the documents themselves. They apply to accuracy and precision runs of QC samples at each concentration level, within a run and between runs.

Assay and level	CV may not exceed	Stated in
Chromatographic assay, QC levels	15%	FDA 2018 Table 1; ICH M10 section 3.2.5.2
Chromatographic assay, at the LLOQ	20%	FDA 2018 Table 1; ICH M10 section 3.2.5.2
Ligand-binding assay such as ELISA, QC levels	20%	FDA 2018 Table 1; ICH M10 section 4.2.4.2
Ligand-binding assay, at the LLOQ and ULOQ	25%	FDA 2018 Table 1; ICH M10 section 4.2.4.2

ICH M10, section 3.2.5.2: “The precision (%CV) of the concentrations determined at each level should not exceed 15%, except at the LLOQ, where it should not exceed 20%.” Section 4.2.4.2, for ligand-binding assays: “Within-run and between-run precision of the QC concentrations determined at each level should not exceed 20%, except at the LLOQ and ULOQ, where it should not exceed 25%.” The FDA guidance (May 2018) gives the same figures in Table 1, as “± 15% CV, except ± 20% CV at LLOQ” for chromatographic assays and “± 20% CV, except ± 25% at LLOQ, ULOQ” for ligand-binding assays.

Sources: FDA, Bioanalytical Method Validation Guidance for Industry (May 2018) and ICH M10, Bioanalytical Method Validation and Study Sample Analysis (Step 4, 24 May 2022). These documents have more requirements than the CV. Follow the version and the SOP that apply to your study.

Worked example: a QC check

A mid-level quality control sample was measured five times in one run (ng/mL): 48.2, 51.5, 49.8, 52.3, 47.9. The mean is 49.94, the sample SD is 1.950 and the CV is 3.90%. That does not exceed 15%, the limit for chromatographic assay QC levels, so the run passes on precision.
An LLOQ sample measured five times gave 1.05, 0.93, 1.12, 0.88, 1.02 ng/mL: mean 1.000, CV 9.57%. That is within the 20% allowed at the LLOQ and also within 15%. Guidance judges precision per concentration level, so each level gets its own CV.

Excel and Google Sheets

With your data in A1:A10, the sample CV is =STDEV.S(A1:A10)/AVERAGE(A1:A10) and the population CV is =STDEV.P(A1:A10)/AVERAGE(A1:A10). Format the cell as a percentage. The calculator above copies the matching formula for the SD you selected. In Python, scipy.stats.variation(x, ddof=1) gives the sample CV; its default is ddof=0, the population version.

To see how a single value compares with the mean in SD units, use the z-score calculator. To see the spread of a data set as quartiles, try the box plot generator, and to express a difference between two means in SD units, use the effect size calculator. To watch a process over time, put the readings on a control chart.