Relative Error Calculator
Compare an observed estimate against a positive reference using absolute percentage error.
How the result changes
Only estimated value changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Relative Error Calculator: Compare an observed estimate against a positive reference using absolute percentage error. Enter estimated value, reference value; the reported quantities are absolute relative error (%), signed error (units). The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
relative error = |estimate - reference| / reference × 100
Worked example
With Estimated value: 98 units, Reference value: 100 units, absolute relative error is 2 %.
Method and inputs
Subtract the reference value from the estimate to obtain signed error. Take its magnitude and divide by the positive reference to scale the discrepancy; multiply by one hundred for a percentage. The signed output preserves whether the estimate is high or low.
Worked example
An estimate of 98 against a reference of 100 differs by -2 units. Its absolute relative error is 2/100 × 100 = 2 percent. If the estimate is 102 instead, the absolute percent stays 2 while signed error becomes positive.
An error of two units against a reference of 100 is 2 percent; the same two-unit error against a reference of 10 is 20 percent. Relative error is therefore sensitive to scale, which is useful when comparing unlike magnitudes but dangerous near zero.
How to read the result
Percent error expresses a discrepancy relative to the selected reference, so changing the reference changes the percent even if the absolute difference is fixed. It is useful for comparing errors across different scales.
An estimate of 98 against reference 100 has signed error -2, indicating underestimation. Reporting only the 2-percent magnitude loses that direction. In calibration work, inspect both average signed error and spread across many measurements to detect bias.
Assumptions and checks
The reference must be strictly positive in this form. A zero reference makes a relative percentage undefined, and negative reference conventions differ by field. The reference should be a trusted benchmark rather than an arbitrary comparison point.
Do not divide by the estimate if the reference is the intended baseline. Also avoid calling an absolute relative error an accuracy score; a 2-percent error does not by itself establish measurement uncertainty or model reliability.
Common questions
What does the relative error calculator calculate?
It returns absolute error as a percentage of the positive reference and the signed difference in original units.
When should I recalculate or check another method?
Recalculate if the benchmark is revised. For references near zero, an absolute error in original units often communicates the discrepancy better than a very large percentage.
Inputs
- Estimated value (units)
- Reference value (units)