Free · Dispersion and variability

Relative Standard Deviation Using Absolute Mean

Express a nonnegative standard deviation as a percentage of the magnitude of a nonzero mean.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A standard deviation of 5 and mean of 100 give relative standard deviation of 5%. A mean of −100 gives the same percentage because this definition uses absolute mean.

RSD (%) = standard deviation ÷ |mean| × 100

Worked example

Enter these known values and leave the other values blank.

Mean — signed input: 100
Standard deviation: 5

Relative standard deviation: 5 %

Assumptions and limitations

The mean must be nonzero; standard deviation and RSD must be nonnegative. The ratio becomes sensitive to small changes when the mean is near zero.
Use consistent units and a meaningful ratio scale. A percentage of mean is not generally comparable across scales with arbitrary zero points, such as Celsius and Fahrenheit.
Enter the mean explicitly. This model can solve for SD or RSD, but cannot recover a signed mean from those two values alone.

Common questions

Why take the absolute value of the mean?

It keeps relative standard deviation nonnegative. The signed coefficient of variation is a different convention.

Can a constant dataset have RSD of zero?

Yes, when its standard deviation is zero and its mean is nonzero.

References

Require a nonzero mean and nonnegative relative standard deviation; near-zero means remain numerically sensitive.

Explore dispersion and variability or browse all statistics calculators.