Work out the relative standard deviation (RSD), also called the coefficient of variation. Enter your values to get the RSD as a percentage, along with the mean and standard deviation.
Standard deviation 3.1623 relative to a mean of 14.
Mean14
Std dev3.1623
Count5
RSD expresses the spread of the data as a percentage of the mean, so you can compare variability between data sets of different sizes.
The relative standard deviation (RSD), or coefficient of variation, shows how spread out a set of values is compared with its average. Because it is a percentage, it lets you compare the consistency of different measurements even when they are on completely different scales — which is why it is common in labs, quality control and finance.
How RSD is calculated
RSD % = (standard deviation ÷ mean) × 100 Sample SD = √( Σ(x − mean)² ÷ (n − 1) ). Choose "Population" to divide by n instead.
Worked example
For 10, 12, 14, 16, 18 the mean is 14. The sample standard deviation is √(40 ÷ 4) = 3.1623, so RSD = (3.1623 ÷ 14) × 100 = 22.59%.
Sample vs population
Use the sample standard deviation (dividing by n − 1) when your data is a sample drawn from a larger group, which is the usual case. Use the population version (dividing by n) only when your values are the entire population. The choice changes the SD and therefore the RSD slightly.
Frequently asked questions
Is RSD the same as coefficient of variation?
Yes. RSD and the coefficient of variation (CV) are the same measure — the standard deviation as a percentage of the mean.
What is a good RSD?
It depends on the field. In analytical chemistry an RSD under 2% is often expected for precise methods, while looser tolerances apply elsewhere.
Can RSD be used with negative numbers?
It is only meaningful when the mean is positive. With a mean near zero or negative, RSD becomes unstable or undefined.
Should I use sample or population SD?
Sample (n − 1) in almost all cases, unless your data covers the entire population you care about.
How do I find standard deviation on a calculator?
On a scientific calculator, switch to statistics (SD or STAT) mode, enter each value followed by the data key (often M+ or DATA), then press the σ key: σₙ for population or σₙ₋₁ (sometimes sx) for sample standard deviation. This tool does it for you — just paste your numbers above.
