# Relative Standard Deviation Calculator

Enter a data set or the standard deviation and mean if known to calculate relative standard deviation using the calculator below.

Separate numbers using a comma (,)

## How to Calculate Relative Standard Deviation

Relative standard deviation, or RSD, is a measure of how closely the data is clustered around the mean in a sample or population. More simply, it is a ratio of the standard deviation to the mean of a data set, and it’s often used to evaluate how close the data within the standard deviation are to the mean.

The relative standard deviation is a statistical measure that is equal to the absolute value of the coefficient of variation. Because it’s an absolute value, the RSD will always be positive.

### Relative Standard Deviation Formula

Because the relative standard deviation is a ratio, you can find it using the ratio formula.

Thus, the formula to calculate the coefficient of variation (CV) is:

RSD = |σμ|

Where:
RSD = relative standard deviation
σ = standard deviation
μ = mean

The formula states that the relative standard deviation RSD is equal to the absolute value of the standard deviation σ (pronounced sigma) divided by the mean μ (pronounced mu).

The relative standard deviation can also be expressed as a percentage. To express RSD in percent form, multiply by 100, then add a percent symbol (%).

percent form = RSD × 100%

For example, let’s calculate the relative standard deviation given a standard deviation of 1.2 and a mean of 14.6.

RSD= |1.214.6|
RSD = 0.082

In this example, the relative standard deviation is equal to 0.082.

To express RSD as a percentage, multiply it by 100.

0.082 × 100 = 8.2

In this example, the relative standard deviation is equal to 0.082 or 8.2%.

Try our statistics calculator for more measurements of a dataset.