How to Calculate Percent Error

The Formula

Percent error equals the absolute difference between the experimental and accepted values, divided by the accepted value, multiplied by 100. Written as: Percent error = (|Experimental - Accepted| / |Accepted|) x 100. The accepted value is always the denominator, never the experimental value.

A Complete Worked Example

Suppose the accepted yield of a reaction is 50 grams and you measured 53 grams. Subtract: 53 minus 50 is 3. Take the absolute value: 3. Divide by the accepted value: 3 divided by 50 is 0.06. Multiply by 100: 6 percent. Your result is 6 percent above what it should have been, and the error is 3 grams.

Why the Absolute Value Matters

The absolute value makes the error positive whether you overshot or undershot. Without it, measuring 47 against an accepted 50 would give a negative percent error, which is meaningless as a measure of error size. If you need to know the direction, calculate the signed version separately or simply state whether your reading was high or low.

Why the Accepted Value Is the Denominator

The accepted value represents the ideal, so the error is measured relative to the ideal and not to your own attempt. This also makes percent error comparable between experiments of different sizes. A 3 gram error is significant against a 50 gram target and negligible against a 5 kilogram one, and the percentage captures that automatically.

How Many Significant Figures to Report

Quote the percent error to two or three significant figures, not the full precision your calculator produces. An answer written as 6.00 percent is clearer than 6.000000 percent and implies the same measurement quality. If the accepted value was only known to one decimal place, the percent error cannot honestly be quoted to five.

Common Mistake One: Dividing by the Wrong Value

Dividing by the experimental value is the most common error. Against an accepted 50 and experimental 53, dividing by 53 gives 5.66 percent rather than the correct 6 percent. The rule is simple: the denominator is always the accepted value.

Common Mistake Two: Forgetting the Multiply by 100

Dividing by the accepted value gives the relative error, a decimal. Reporting 0.06 as the percent error leaves out the final step and is off by a factor of 100. If your answer comes out as a small decimal, you have probably stopped one step early.

Common Mistake Three: Rounding Too Early

Rounding the accepted value or the absolute error before dividing shifts the final answer at exactly the precision you care about. Carry full precision through every step and round only the number you intend to report.

What Counts as an Acceptable Percent Error

It depends on the experiment. Many undergraduate labs set targets under 5 percent, and under 1 percent is generally strong. Reactions involving multiple steps often run 5 to 10 percent, while directly measured physical constants such as standard gravity can be measured far more precisely. Ask what your course expects rather than assuming a universal threshold.