absolute error
/ AB-suh-loot EHR-ur /
If a bathroom scale says you weigh 70 kg but the true value is 72 kg, the scale is simply '2 kg off.' That plain, unscaled gap — measured in the same units as the thing itself — is the absolute error. It answers the most direct question you can ask of a measurement: by how much did it miss?
Absolute error is the difference between a measured value and the true (or accepted) value, carried with its sign and its units: measured minus true. A positive absolute error means the reading came out too high, a negative one too low. Because it keeps the original units (grams, millilitres, degrees), it tells you the size of the miss in concrete terms, but it does not tell you whether that miss is large or small relative to what you were measuring.
Absolute error matters as the raw building block of accuracy and the starting point for relative error. The honest caveat is exactly that limitation: a 2 kg error is trivial when weighing a person but catastrophic when weighing a letter. Absolute error alone cannot judge how serious a miss is — for that you must compare it to the size of the measurement, which is what relative error does.
A standard weight is certified at 1.0000 g, and a balance reads it as 0.9994 g. The absolute error is 0.9994 − 1.0000 = −0.0006 g — six tenths of a milligram low, expressed in the same units as the mass.
Same units as the measurement, sign included.
Keep the sign: a +0.5 mL error and a −0.5 mL error are different problems. Some texts use the absolute value when only the magnitude of the miss matters.