PercentChangeFormula

Percent Error Formula & Calculator

How far a measured value is from the accepted value, as a percentage of the accepted value.

Percent error = |measured − accepted| ÷ |accepted| × 100
2.1407% error
  1. Error = |9.6 − 9.81| = 0.21
  2. 0.21 ÷ |9.81| × 100 = 2.1407%

How to calculate percent error

  1. Subtract the accepted (true) value from your measured value.
  2. Take the absolute value, so the error is positive.
  3. Divide by the accepted value and multiply by 100.

Examples

ExperimentMeasuredAcceptedWorkingPercent error
Gravity (m/s²)9.69.810.21 ÷ 9.81 × 1002.141%
Volume in a beaker (mL)48.5501.5 ÷ 50 × 1003%

Percent error vs. percent change

The arithmetic is the same shape as percent change: a difference divided by a reference value. The difference is in meaning. With percent error the reference is the correct value and the sign is usually dropped; with percent change the reference is the earlier value and the sign tells you the direction.

Sources of error to mention in a lab report

  • Random error: scatter from reading instruments, timing by hand or small changes in conditions. Reduce it by repeating the measurement and averaging.
  • Systematic error: a consistent bias, such as a scale that isn’t zeroed or an uncalibrated thermometer. Repeating doesn’t fix it; recalibrating does.
  • Rounding: keep full precision until the final step, then round the percent error.

Frequently asked questions

What is the percent error formula?

Percent error = |measured value − accepted value| ÷ |accepted value| × 100.

Can percent error be negative?

With the absolute-value formula, no. Some science courses drop the absolute value to show whether the measurement was too high (positive) or too low (negative); check which convention your course uses.

What is a good percent error?

It depends on the experiment. In many school labs, under about 5% is considered good, but precise instruments and professional work expect far smaller errors.

How is percent error different from percent difference?

Percent error compares a measurement to a known correct value and divides by that correct value. Percent difference compares two values when neither is known to be correct and divides by their average.