MATH CALCULATOR

Percent Error Calculator

Compare a measurement with a nonzero reference value to calculate absolute percent error and the direction of the difference.

Calculator

Must be nonzero. Use the same unit as the measurement.
YOUR RESULTS
Absolute percent error5 %
Measured minus reference
-0.5
Absolute difference
0.5
Signed error relative to reference magnitude
-5 %
Comparison
Below reference

Understanding your result

Absolute percent error is nonnegative. The signed result divides measured-minus-reference by the reference magnitude, so positive means numerically above the reference even when the reference itself is negative.

The formula

Absolute percent error = |measured − reference| ÷ |reference| × 100. Signed magnitude-relative error = (measured − reference) ÷ |reference| × 100.

The reference supplies the scale for the comparison. Taking its absolute value keeps the error magnitude nonnegative. A zero reference cannot supply a relative scale, so the calculator reports an input error instead of infinity or a misleading zero.

Worked example

A measured value of 9.5 compared with an accepted value of 10 differs by −0.5. The absolute percent error is 0.5 ÷ 10 × 100 = 5%. The signed result is −5%, indicating a measurement below the reference.

How to use this calculator

  1. Enter the experimental value and accepted reference in matching units.
  2. Check that the reference is nonzero and appropriate to the experiment.
  3. Use the absolute error for magnitude and the signed result for direction.

Error and difference answer different questions

Percent error treats one value as a reference. Percent difference instead compares two values symmetrically, often using their average as the denominator. Swapping the inputs in percent error therefore changes the result. For example, comparing 9 against 10 gives 10%, while comparing 10 against 9 gives about 11.111%.

Interpret small and negative reference values carefully

A reference close to zero can produce a large percentage from a small absolute difference. Review the absolute difference alongside the percentage before drawing conclusions. For negative references, signed-error conventions vary between courses and reporting standards. This page states its magnitude-denominator convention explicitly; follow a requested convention when preparing a laboratory report.

Assumptions & limitations

What this calculation assumes

  • One value is a meaningful accepted reference and both use the same physical or numerical scale.

What to keep in mind

  • No uncertainty budget, confidence interval, instrument calibration, or pass/fail tolerance decision.

Common questions

Can percent error exceed 100%?

Yes. It exceeds 100% whenever the absolute difference exceeds the magnitude of the reference.

Does a 5% error mean the measurement is acceptable?

Not by itself. Acceptability depends on the experiment, measurement uncertainty, and specified tolerance.

Sources & further reading