Percent error: the formula and how to use it in lab reports

Percent error tells you how far a measurement is from the accepted (or theoretical) value, as a share of that accepted value.

Worked example

You measure the acceleration due to gravity as 9.62 m/s². The accepted value is 9.81 m/s².

1. Difference: 9.62 − 9.81 = −0.19
2. Absolute value: 0.19
3. Divide by the accepted value: 0.19 ÷ 9.81 = 0.01937
4. Multiply by 100: 1.94%

Why the absolute value?

Percent error usually describes the size of the error, not its direction. Measuring 10.00 m/s² (0.19 too high) gives the same 1.94% error as 9.62 m/s² (0.19 too low). If your course wants the direction, it will ask for “signed percent error”, and you skip the absolute value: 9.62 gives −1.94%.

Why divide by the accepted value?

The accepted value is the reference you’re judging against. Dividing by your measurement would make the error depend on how wrong you were, which is circular. It also gives a different number: 0.19 ÷ 9.62 = 1.98%.

Percent error vs percentage difference

Use percent error when one value is accepted as correct (a known constant, a manufacturer’s specification, a theoretical prediction).

Use percentage difference when you’re comparing two measurements and neither is the reference, such as two lab groups measuring the same thing. It divides by the average of the two values. See percentage change vs percentage difference.

Writing it up

A typical lab report sentence: “Our measured value of g was 9.62 m/s², a percent error of 1.94% from the accepted value of 9.81 m/s².” Then discuss likely sources of error: reaction time with a stopwatch, air resistance, measuring the drop height.

Keep the rounding sensible. If your measurement has three significant figures, reporting the error as 1.936799% suggests more precision than you have. Two or three significant figures (1.9% or 1.94%) is usually right.

When the accepted value is zero

Percent error is undefined if the accepted value is zero, because you’d divide by zero. Report the absolute error instead (for example, “the reading was 0.03 V when it should have been 0 V”).

Other examples

Density. Measured 2.65 g/cm³, accepted 2.70: |2.65 − 2.70| ÷ 2.70 = 1.85%.

Boiling point. Measured 98.6 °C, accepted 100.0 °C: 1.4 ÷ 100 = 1.4%. (Percent error on a temperature in Celsius is a convention that’s commonly used in labs, even though Celsius zero is arbitrary.)

For more on dividing by the right base, see test score percentage, and for why rounded percentages can disagree, see why percentages don’t add to 100.

Questions