Signed vs Absolute Percent Error
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Direct answer
Absolute percent error reports magnitude. Signed relative error preserves the sign of measured minus reference and indicates whether the measurement is above or below the reference, subject to the reference sign convention.
Formula and method
Signed = (measured−reference)/reference × 100; absolute magnitude = |measured−reference|/|reference| × 100
The calculation keeps full precision through the formula and rounds only the displayed answer.
Step-by-step calculation
- Calculate measured−reference.
- Preserve the sign for directional bias.
- Use absolute values for magnitude.
- Label both outputs rather than calling both simply percent error.
Worked examples
High result
104 vs 100: signed +4%, absolute 4%.
Low result
96 vs 100: signed −4%, absolute 4%.
Negative reference
Signed interpretation becomes domain-dependent; use explicit labels and the absolute-reference magnitude for error size.
Interpretation and edge cases
- The sign is not a quality grade; it only indicates direction under the formula.
- Averages of signed errors can cancel positive and negative deviations.
- For bias assessment, use repeated measurements and a proper measurement model.
Frequently asked questions
Can absolute percent error be negative?
No.
What does negative signed error mean?
Measured is below reference when the reference is positive.
Which should a calculator headline?
Absolute percent error, with signed relative error as a separate diagnostic.
Sources and transparency
The formulas and examples were evidence-checked on 2026-09-10. This is educational mathematical content. It does not replace a field-specific standard, accounting policy, laboratory method, contractual definition or professional judgment.
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