Compare a measured value against the true value as a percent error.
Percent error quantifies the accuracy of a measurement by expressing how far it deviates from the accepted value as a fraction of that value. A small percent error means the measurement is close to the true value. The sign tells you the direction of the error: positive means you overestimated, negative means you underestimated.
Signed percent error
% Error = (Measured − Actual) / |Actual| × 100
Absolute error
Absolute Error = Measured − Actual
It depends on the field. In most high-school lab work, an error below 5% is considered acceptable. In analytical chemistry, 1% or below is typical. In particle physics, errors below 0.01% are expected. Always check the tolerance specified by your experiment or industry standard.
Use the signed result (which can be negative) when the direction matters — overshooting versus undershooting the true value are different kinds of systematic error. Use the unsigned (absolute) form when you only care about the magnitude, which is what most textbook problems ask for.
Percent error divides by the actual value. Division by zero has no mathematical definition. If the accepted value is zero, you can report the absolute error instead, but a percentage has no meaning.
Percent error compares a measurement to a known accepted value. Percent difference compares two measurements of equal standing when neither is the 'truth', dividing by their average instead of one specific value.