Relative Standard Deviation Calculator

What Relative Standard Deviation Is

Relative standard deviation (RSD) expresses standard deviation as a percentage of the mean. It answers whether a spread is large or small compared with the typical value. Quality control, assay precision, and comparing datasets with different units all use RSD. Related tools: Coefficient of Variation Calculator and Standard Deviation Calculator.

RSD Formula

$$\text{RSD} = \frac{\sigma}{|\mu|} \times 100\%$$

The absolute value of the mean keeps RSD positive even when the mean is negative. A common report format is $\mu \pm \text{RSD}\%$. For measurement error as a fraction of a true value, use the Relative Error Calculator.

RSD vs Coefficient of Variation

Coefficient of variation divides standard deviation by the signed mean, so it can be negative. RSD divides by the absolute mean, so it is always non-negative. For most lab and quality reports, RSD is the percentage form people expect.

When Not to Use RSD

Do not use RSD when zero is an arbitrary point, such as temperature in Celsius. A mean near 0°C inflates RSD even if the spread is unchanged. Convert to a ratio scale first, such as kelvin, or stay with the raw standard deviation.

Example

A batch has mean 48.5 and standard deviation 3.2. Then $\text{RSD} = 3.2 / 48.5 \times 100\% \approx 6.60\%$, written as $48.5 \pm 6.60\%$.