Complete guide
Percent error calculator with signed difference
Enter an observed result and the accepted reference. Calculator24 shows absolute percent error, signed error, raw difference and whether the observation is above or below the reference.
How to calculate percent error
Subtract the accepted value from the observation, divide by the magnitude of the accepted value and multiply by 100. Absolute percent error discards direction; signed error preserves it.
Percent error formula
Use the accepted magnitude in the denominator so a negative reference does not reverse the meaning of the percentage scale.
signed error % = (observed−accepted)/|accepted| × 100absolute error % = |observed−accepted|/|accepted| × 100Positive and negative error
A positive signed result means the observation is above the accepted value. A negative result means it is below. The absolute result is useful when only magnitude matters.
Zero accepted value
Division by zero is undefined. When the reference is zero, report the absolute difference or use an error measure designed for that context.
Accuracy and precision
A small percent error indicates closeness to the chosen reference. It does not by itself measure repeatability, uncertainty or whether the reference is correct.
Error measures
| Measure | Keeps direction | Reference |
|---|---|---|
| Signed percent error | Yes | Accepted magnitude |
| Absolute percent error | No | Accepted magnitude |
| Absolute difference | Yes as sign | No denominator |
Frequently asked questions
What is percent error?
It is the difference from an accepted value expressed as a percentage of that reference magnitude.
Can percent error be negative?
Signed percent error can; absolute percent error cannot.
Why use the absolute accepted value?
It keeps the denominator positive while direction remains in the numerator.
What if the accepted value is zero?
Percent error is undefined because division by zero is impossible.
Is percent error the same as percent difference?
No. Percent difference treats both values symmetrically and uses their average magnitude.
What to keep in mind
Percent error is undefined when the accepted value is zero. Preserve meaningful measurement precision when reporting.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.