Percent error

Before you rely on it

What to check

The theoretical value goes in the denominator. Not the measured one.

The common error

Where people go wrong with percent error

Putting the measured value in the denominator. The answer changes, and it changes more the further apart the two values are.

Worked through

Percent error in plain numbers

A student measures the acceleration due to gravity in a lab and gets 9.60 meters per second squared; the accepted value is 9.81. The error is 9.60 − 9.81 = −0.21, and the percent error is |−0.21| ÷ 9.81 × 100, which is 2.1%. If the measurement had been 10.02, the error would be +0.21 and the percent error the same 2.1%, since the absolute value ignores direction; some fields keep the sign to show whether the result runs high or low. Percent error tells you how far off you were relative to the true value, which puts small and large quantities on one scale.

Easily confused

Percent error and its neighbours

Percent error is not percent difference or percent change. Percent error compares an experimental value with a known or accepted one, dividing by the accepted value. Percent difference compares two experimental values with no true value, dividing by their average. Percent change compares an old and a new value in time. Relative error is the same as percent error without the times 100. Absolute error is the raw difference in units. Choose the one that matches whether you have a true reference.

In real decisions

Where percent error turns up

Science and engineering classes use it to judge how well an experiment matched theory. Quality control uses related measures to check instruments against standards. Calibration checks compare readings with reference weights or temperatures. Manufacturers examine it when parts must stay within tolerance; a small percent error suggests a careful experiment, and a large one prompts a search for systematic problems in the method.

Know the edges

Where percent error stops being reliable

It requires a trusted true value, which is not always available; a small percent error does not prove the method is right, since errors can cancel. Measurements near zero produce huge percentages. Random and systematic errors have different causes. Report uncertainty as well, and repeat measurements to see whether the error is consistent.

Quick answers

What people ask about percent error

Is percent error always positive? In the usual definition, yes, since it uses the absolute value. Some fields keep the sign to show whether the result was high or low.

What is an acceptable percent error? It depends on the experiment. Classroom labs often accept five to ten percent. Precision instruments aim far lower. Compare with the uncertainty of the method.

What if the accepted value is zero? Percent error is undefined because you would divide by zero. Use absolute error instead, or another measure of accuracy.

What causes percent error? Instrument limits, technique, environmental changes and rounding. Random errors scatter results. Systematic errors push them the same way each time.