How this calculator works
Error compares a result with a specified reference. Absolute error keeps only the size of the difference; signed error also records direction. Division by the reference magnitude produces a dimensionless ratio. The reverse reference mode assumes a positive reference because an unsigned percentage alone cannot determine both direction and sign. Error is distinct from uncertainty, which describes the dispersion of values reasonably attributable to a measurement.
Formula
e = observed - reference; relative error = |e|/|reference|; signed relative error = e/|reference|.
Worked example
An observed value of 102 against 100 gives signed error 2 and relative error 2%. A result of 9 against 10 gives signed error -1 and relative error 10%.
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Frequently asked questions
Why use a non-zero reference?
A relative comparison needs a denominator. Absolute error is still meaningful at a zero reference, but relative error is undefined.
Can relative error exceed 100%?
Yes. The absolute discrepancy can be larger than the reference magnitude.
Is error the same as uncertainty?
No. Error refers to a difference from a reference; uncertainty expresses limited knowledge of the measured quantity.