Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
What percent error measures
Percent error compares a measured value with an accepted or theoretical value by scaling the absolute difference to the size of the theoretical value:
Where is the experimental value and is the theoretical value. The calculator also reports absolute error and signed error so you can see both the size and the direction of the difference.
How to interpret the result
A smaller percent error means the measurement is closer to the reference value, but there is no universal “good” cutoff for every field. What counts as acceptable depends on the method, instrument, tolerance, and purpose of the measurement.
If the theoretical value is zero, percent error is undefined because the formula would divide by zero. In that case, use the absolute error or a domain-specific metric instead of forcing a percentage that has no mathematical meaning.
Frequently asked questions
Why does the formula use absolute value?
Absolute value makes the main percent-error result describe the size of the miss regardless of direction. The calculator still shows signed error separately so you can tell whether the measurement was high or low.
What if the theoretical value is zero?
Percent error is undefined when the theoretical value is zero because the formula divides by the reference value. Use absolute error or another metric that fits the experiment.
Is less than 5% always good?
No. The acceptable range depends on the field, instrument, and tolerance requirement. A classroom lab and a calibrated manufacturing process may use very different standards.
Why show both signed and absolute error?
Absolute error shows the size of the difference. Signed error shows direction: a positive value means the measurement is above the reference, and a negative value means it is below.
