# Relative Standard Deviation Calculator

Created by Jasmine J Mah
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Mar 10, 2020

Once you know the standard deviation and mean of your dataset, the RSD calculator (relative standard deviation calculator) helps you make decisions about that data. Is the variance 'great' or 'small'? How does your data compare to other datasets? Read on to learn more.

## What is the relative standard deviation?

The relative standard deviation, or RSD, is a form of standard deviation, where it is presented as a percentage of the mean. The RSD is always positive.

Using the relative standard deviation formula, you can easily calculate RSD by dividing the standard deviation by the absolute value of the mean, then multiplying the result by 100 to represent it as a percentage:

relative standard deviation = (standard deviation / |mean|) * 100%

It is common to write the relative standard deviation after the mean and with a plus-minus sign, e.g., 25 ± 2%, where ± 2% is the relative standard deviation.

## Common uses for the RSD calculator

Relative standard deviation puts the standard deviation into perspective by comparing it to the mean. Viewing standard deviation as RSD helps people make decisions in a variety of situations, including:

• Quality assurance, e.g., a grocery store may require the RSD of all fruit sizes to be less than 10%.
• Evaluating the volatility of stock prices.
• In analytical chemistry, to express the precision of an assay.
• Comparing the variation of two different datasets.

## When not to use relative standard deviation

It is not appropriate to use the relative standard deviation calculator for situations in which 0 does not represent an absence of quantity, such as temperature in degrees Celsius or Fahrenheit.

For example, if the average temperature was 12 ± 3°C on one day and 1 ± 3°C the next day, the RSD would be 25% on the first day and 300% (an enormous increase!) on the second day.

Since 0°C is arbitrary, having a mean temperature closer to 0 shouldn't necessarily make deviations from the mean seem greater. Instead, relative standard deviation could be calculated for temperatures expressed in Kelvin.

## Relative standard deviation and coefficient of variation

The relative standard deviation formula is very similar to the coefficient of variation calculation. The only difference is that the RSD calculator divides the standard deviation by the absolute value of the mean, while the coefficient of variation calculation divides the standard deviation by the mean. As a result, the coefficient of variation can be either positive or negative, while the relative standard deviation is always positive.

## Comparing apples and oranges (and pineapples!) - An example

David wants to stock his fruit stand with a new and exciting item. He can choose from a box of apples, a box of oranges, or a box of pineapples. However, he wants to make sure that the fruits are consistent in weight for easy pricing. The mean and standard deviation of weight for each fruit is:

• Apples: 100 ± 5 g.
• Oranges: 120 ± 30 g.
• Pineapples: 2 ± 0.5 lbs.

Which fruit has the most consistent weight? For apples, the calculation would be:

(5 g / 100 g) * 100% = 5%

Try using the RSD calculator to convert the standard deviations into relative standard deviations.

Now we can see the mean and RSD of weight for each fruit:

• Apples: 100 g ± 5%
• Oranges: 120 g ± 25%
• Pineapples: 2 g ± 25%

With the standard deviation expressed as relative standard deviation, David can now see that apples have the most consistent weight.

Jasmine J Mah
Mean
Standard deviation
Relative standard deviation
%
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