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Absolute error
Intermediate
Magnitude of the difference between measured and true value.
Δa = ∣a_measured − a_true∣Absolute error is the size of the difference between a measured value and the true (or mean) value, in the same units as the measurement. It tells how far off you are but not how serious that is relative to the size of the quantity.
True length 50.0 cm, measured 49.6 cm: absolute error = 0.4 cm.
An error of 1 cm is huge for a pencil but negligible for a road. Use relative error to compare.
In more detail
The absolute error is the size of the uncertainty in a quantity, given in the same units as the measurement. A reading of 12.0 ± 0.2 cm has an absolute error of 0.2 cm.
Real-world uses
- A lab report quotes each measured value with its absolute error so readers can judge the result.
- Medical dosing tolerances are stated as absolute limits in milligrams.
- A quality inspector checks that a machined part is within 0.05 mm of its drawing dimension, which is an absolute error limit.
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Frequently asked questions
How do I estimate the absolute error of a single reading?
Usually take half of the smallest division of the instrument, or the least count if the instrument reads that precisely.
Is absolute error the same as a mistake?
No. It is the expected uncertainty of the measurement, not an error made by the experimenter.
Can an absolute error be negative?
No. Absolute error is a magnitude, so it is always zero or positive. The sign of the difference is lost by using the absolute value.
Related topics in Measurement & Math Tools
Accuracy vs precision · Systematic error · Random error · Relative and percent error · Error in a sum or difference · Error in product or quotient