Percent error answers one question every experiment asks: how close did my measurement come to the value it should have been? It rescales the raw gap between your result and the accepted value into a percentage, so a 0.05 g/cm³ miss on a density of 2.70 reads as a clear 1.85% — comparable across experiments, instruments, and units. This calculator reports percent, absolute, and relative error together, handles the signed and edge cases, and tells you in plain language whether the agreement is good.

Percent error in the lab

In chemistry, physics, and engineering labs, percent error is the standard way to grade a measurement against a known quantity — the accepted density of a metal, the theoretical yield of a reaction, the published value of gravitational acceleration. Because it is a percentage, it lets you compare a tiny measurement and a huge one on the same scale: 1% error is 1% error whether you measured milligrams or kilometres. A common rule of thumb is that under 5% is good, 5–10% is acceptable but worth examining, and 10% or more points to a systematic problem.

Accuracy vs precision

Percent error measures accuracy — how close your result is to the true value. It says nothing about precision, which is how close repeated measurements are to one another. A scale that always reads 2% high is precise (consistent) but not accurate; a wobbly measurement that happens to average out can be accurate on average but imprecise. A low percent error on a single trial is encouraging, but only repeated trials reveal whether your method is also precise.

Why you divide by the theoretical value

Percent error always divides by the theoretical (accepted) value, not the measured one, because the accepted value is treated as the reference truth. Dividing by it answers "how far did my measurement stray from the correct answer, as a fraction of that answer?" If you divided by the experimental value instead, the denominator would change every time you re-measured, so two runs of the same experiment could report different errors for the same true discrepancy. Using a fixed reference keeps results comparable.

Signed vs absolute error

By default percent error is reported as a positive number — the absolute form — because usually you only care how far off you were, not which way. The signed form keeps the direction: a positive value means your measurement came in high, a negative value means it came in low. Signed error is useful when you are hunting a systematic bias — if every trial reads a few percent low, that consistent negative sign points to a calibration offset rather than random scatter. One edge case to watch: when the accepted value is zero, percent error is undefined (division by zero), and you should report the absolute error instead.