Percent Relative Standard Deviation

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The Percent Relative Standard Deviation calculator computes the percent relative standard deviation based on the standard deviation for a sample and the mean for the sample.

INSTRUCTIONS: Enter the following:

(σ) Sample Standard Deviation
(`barx`) Sample Mean

Percent Relative Standard Deviation (%RSD): The calculator returns the percent.

The Math / Science

The percent relative standard deviation (%RSD) is also known as the coefficient of variation (CV). The %RSD is a measure of the dispersion of a probability distribution. Dividing the standard deviation by the mean of the data provides the relative magnitude of the standard deviation. This equation returns the %RSD as the percentage; i.e. an RSD for `sigma` = .05 and a `barx` = 1.0 should give you 5.0 percent as the output.

The equation for the Percent Relative Standard Deviation is :

%RSD = `sigma / barx` x 100%

where:

`sigma` = standard deviation for the sample
`barx` = mean for sample

The formula for statistical mean is the sum of observations divided by the number of observations as follows:

`barx = (sum_1^n(x_n))/n`

where:

`barx` is the statistical mean
x_n are the observations
n is the number of observations

The formula for sample standard deviation:

`sigma = sqrt((sum_1^n(x_n-mu)^2)/(n-1))`

where:

σ is the standard deviation (sample or population)
n is the number of observations
μ is the statistical mean

This equation is also represented in the Science/Chemistry/Analytical domain

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