The formula
How to calculate coefficient of variation
The coefficient of variation expresses standard deviation as a percentage of the mean. Because it cancels out the units, it lets you compare the variability of things measured on completely different scales.
It is the standard measure of relative dispersion in analytical chemistry, quality control and finance, where it is used to compare the volatility of assets with very different price levels.
What to enter:
- Mean
- Standard deviation
The result updates on every keystroke. The URL updates too, which makes the filled-in version easy to bookmark or send to someone else.
The calculation runs on exactly the numbers currently in the fields above, recomputed in full each time — there is no dependency on the order values are entered in, so adjusting one input to test a scenario and then changing it back leaves the result exactly where it started.
Why coefficient of variation matters
This kind of calculation comes up in coursework, in a laboratory or field setting, and in professional practice, and the arithmetic is identical in every case — only the numbers being fed into it, and what is riding on getting them right, actually change.
Beyond a single check, the same calculation is worth rerunning whenever a measured input changes — a new reading, a corrected value, an updated assumption — since the result here always reflects exactly what is currently in the fields above rather than a value calculated once and then left stale.
This calculation sits in a long tradition of being done first by hand with tables and slide rules, then with a scientific calculator, and now with a page like this one — the underlying mathematics has not changed at any point in that history, only the speed and convenience of getting from the inputs to the answer. Understanding the formula itself, shown above, is still worth doing even when a tool computes it instantly, since it is what makes the result trustworthy rather than just fast.
It is worth keeping a note of which inputs were used to produce a given result, particularly where the figure is going into a report or a further calculation — reproducing a result later, or explaining how it was reached, is far easier with the original inputs to hand than by trying to reverse-engineer them from the output alone.
Worked example
Here is the calculation with the starting values:
- Mean: 74
- Standard deviation: 11.5
That gives:
- Coefficient of variation: 15.5405 %
- Signal to noise ratio: 6.4348
- As a decimal: 0.1554
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
Below 10% is generally considered low variability, 10–30% moderate, above 30% high. Laboratory assays typically require a CV under 15% to be considered acceptably precise.
Where this goes wrong. The measure breaks down when the mean is near zero, because dividing by a small number inflates the result without limit. It is also meaningless for data on interval scales such as temperature in Celsius, where zero is arbitrary.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Context decides. Under 15% is the usual acceptance criterion for laboratory assays; under 10% is expected in manufacturing quality control; investment returns routinely exceed 100%.
Yes. RSD is the term more common in analytical chemistry, CV in statistics and finance, and both are the standard deviation divided by the mean.
The headline figure is coefficient of variation. With 74 mean and 11.5 standard deviation, that comes to 15.5405 %. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.