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Excel and Relative Standard Deviation %RSD

This guide will detail how to calculated the relative standard deviation (%RSD) using Excel, then walk through a worked example and finally detail the limitations of the calculation. Percentage relative standard deviation is a widely used statistical tool but strangely there is no automated function in any version of Microsoft Excel.

Relative Standard Deviation in Excel 2003, 2007 & 2010

%RSD is a powerful tool to statistically inspect the variation in sets of data but a specific function is not available in Excel 2003, 2007 or even 2010. To calculate the %RSD in Microsoft Excel a short formula must be used:


= (STDEV(Data Range) / AVERAGE(Data Range))*100


= (STDEV(A1:A11) / AVERAGE(A1:A11))*100

Excel Percent Relative Standard Deviation %RSD

The above %RSD example has been entered into the Excel formula bar and will calculate the percent relative standard deviation of the 5 value data set E6 to E11. In the cell where the formula is written a value between 0-100 will be reported. The result is expressed as an percentage, with a low number (<2.5%) indicating a small spread of values and a high value indicating a significant spread of results.

Why is %RSD So Important?

%RSD (relative standard deviation) is a statistical measurement that describes the spread of data with respect to the mean and the result is expressed as a percentage. The %RSD function is popular with non-statisticians as the interpretation is based on a percent result and not some abstract value. The main use for %RSD is in analytical chemistry and is routinely used to assess the variation of sets of data.

%RSD Excel Worked Example

The excel %RSD calculation requires two functions; Average and STDEV. The AVERAGE function [=average(population)] calculates the mean of the data set while the STDEV [=STDEV(population)] calculates the standard deviation (SD) of the data. The final stage of the calculation is to express the result as a percent which the *100 does. This following %RSD example is based upon a data set of 5 values. The image on the left displays the full calculation while the right image displays the numerical values.


Excel Percent Relative Standard Deviation %RSD Excel Percent Relative Standard Deviation %RSD

The short version for the left table is to combine the average and SD calculation into one function and this would read:


The calculation from the previous example would be expressed as:

Excel Percent Relative Standard Deviation %RSD

Relative Standard Deviation Excel Limitations

Percent relative standard deviation is popular but there are limitations to the statistical method. The main limitation is when the average is very small (<1) and a small variation in the set of data will result in a large result. The data set for %RDS must be based around one set of results, it is not applicable when there are different discrete sets of results. The data set must be larger than 5 for a meaningful result.

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