What Is Relative Standard Deviation?

By Staff WriterLast Updated Mar 24, 2020 5:32:31 PM ET

Relative standard deviation (RSD) is the absolute value of coefficient variation and is usually expressed as a percentage. The RSD is often referred to as the coefficient of variation or relative variance, which is the square of the coefficient of variation. The RSD is important for comparing the uncertainty between different measurements of varying absolute magnitude.

Standard deviation, s, is a statistical measure of the precision for values of repetitive measurements. The advantage of using the standard deviation to quote uncertainty is due to the fact that it has the same units as the experimental data. The RSD is computed from the standard deviation, s, and is often expressed as parts per thousand (ppt) or a percentage:

RSD = {s/x) * 1000 ppt –RSD = {S/X} * 100%


RSD = Relative standard deviation

S = Standard deviation

x = mean

The %-RSD is known as the “coefficient of variance” or CV

The RSD shows the spread of data in percentage. The smaller the standard deviation, the closer the numbers are to the average, and vice versa. Standard deviation and relative standard deviation are both measures of precision. Other measures include: variance, standard error and confidence limits. The advantage of using variance is that variance from independent sources of variation may be added up to get variance for a measurement.