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Relative and percent error
Intermediate
Absolute error divided by the measured value.
δ = Δa / aRelative error is absolute error divided by the measured value; multiply by 100 for a percentage. It shows how significant the error is and lets you compare measurements of different sizes.
0.4 cm error on 50.0 cm gives relative error 0.008 or 0.8%.
Use the true or best-estimate value in the denominator, not the error itself.
In more detail
The relative error divides the absolute error by the measured value, and the percent error multiplies that by 100. It shows how significant the uncertainty is compared with the size of the quantity.
Real-world uses
- A 1 mm error is negligible when measuring a 1 m rod, but significant for a 1 cm pin.
- Industries specify tolerances as percentages to compare different products fairly.
- A 1 mm error on a 10 cm pencil is 1 percent, but the same 1 mm error on a 1 m rod is only 0.1 percent, so the relative error shows which measurement is better.
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Frequently asked questions
Why use percent error?
It makes it easy to compare the quality of measurements of very different sizes.
What is percent error compared with percent difference?
Percent error compares a measurement with a known true value. Percent difference compares two measurements with each other.
When should I quote a percentage instead of an absolute error?
Quote a percentage when comparing measurements of different sizes, and an absolute error when the size of the uncertainty itself matters.
Related topics in Measurement & Math Tools
Systematic error · Random error · Absolute error · Error in a sum or difference · Error in product or quotient · Error in powers