How to Calculate Percent Error: The Accuracy Formula for Science

The formula and what it measures

Percent error answers one question: how close did my measurement come to the truth? It is percent error = |experimental − true| ÷ true × 100. The absolute value bars mean you ignore the direction of the miss and report only the size. Dividing by the true value, not the measurement, keeps the reference fixed — the accepted value is what you are being judged against.

A worked example

Suppose a lab measures the density of a metal as 8.60 g/cm³, and the accepted value is 8.96 g/cm³. The absolute difference is |8.60 − 8.96| = 0.36. Divide by the true value: 0.36 ÷ 8.96 = 0.0402. Multiply by 100 to get a percent error of 4.02%. That is a fairly accurate result — the measurement is within about four percent of the reference.

Accuracy vs. precision

Percent error measures accuracy — closeness to the true value — not precision, which is how tightly repeated measurements cluster together. You can be precise but inaccurate: three readings of 8.60, 8.61, and 8.60 g/cm³ are precise, yet each carries the same 4% error against the true 8.96. Reducing percent error usually means fixing a systematic bias, such as a miscalibrated instrument, rather than just repeating the measurement.

Frequently asked questions

Can percent error be negative?

With the absolute value, no — it is always zero or positive. Some fields keep the sign to show whether the measurement was too high or too low, but the standard formula reports the magnitude only.

What is a good percent error?

It depends on the field. A school lab may accept under 5%, while precision engineering demands far less. Always compare against the tolerance expected for your particular experiment.

What if the true value is zero?

Percent error is undefined, because you cannot divide by zero. When the reference is zero, report the absolute error instead, or use a different accuracy measure.

Is percent error the same as percent difference?

No. Percent error divides by a known true value; percent difference divides by the average of two peer values with no accepted reference. Use error when one value is authoritative.