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.

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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, which is a ratio of the standard deviation to the mean.

Because it’s an absolute value, the RSD will always be positive, and it will never be a negative value.

Relative Standard Deviation Formula

Because the relative standard deviation is the absolute value of the coefficient of variation, you can take the absolute value of the CV formula to find it.

Thus, the formula to calculate the relative standard deviation (RSD) is:

RSD=\left |\frac{\sigma}{\mu}\right |

Where:
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 (%).

RSD=\left |\frac{\sigma}{\mu}\right | \times 100\%
Graphic showing the relative standard deviation formula where the RSD is equal to the absolute value of the standard deviation divided by the mean, times 100%

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

RSD=\left |\frac{1.2}{14.6}\right |
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.