Percent Error Calculator

Percent error describes how far an observed or experimental value is from a true, theoretical, or accepted value relative to that reference. It converts an absolute measurement gap into a percentage, making errors easier to compare across experiments with different scales. A difference of one unit may be important when the accepted value is two, but almost negligible when the accepted value is ten thousand. Expressing the gap as a percentage supplies the missing context. The standard formula is the absolute difference between the observed value and accepted value, divided by the absolute accepted value, then multiplied by 100. The absolute values keep the reported error nonnegative. For example, an observed measurement of 9.8 against an accepted value of 10 has an absolute difference of 0.2. Dividing 0.2 by 10 and multiplying by 100 gives a 2 percent error. An observation above the reference and an equally distant observation below it therefore produce the same percent error. Percent error is widely used in laboratory work, engineering tests, quality control, calibration, forecasting, and classroom science. It answers a different question from percentage change. Percentage change tracks movement from an initial value to a later value and preserves whether the movement increased or decreased. Percent error instead treats one number as the benchmark and measures the magnitude of departure from it. It also differs from percentage difference, which treats both values symmetrically and divides by their average. A smaller percent error generally indicates closer agreement with the accepted value, but acceptable error depends on the application. A school experiment may reasonably tolerate several percent because of instrument limits and environmental variation. Precision manufacturing or medical measurements can require much tighter tolerances. Always compare the result with the uncertainty, resolution, and standards that apply to the measurement process. The accepted value cannot be zero in the conventional formula because division by zero is undefined. If the correct reference is zero, report the absolute error or use a domain-specific tolerance instead. Also preserve enough significant figures while calculating, then round the final percentage to a precision justified by the original measurements. This calculator retains useful decimal detail so you can apply the rounding convention appropriate to your work.