What is percentage error?
Percentage error tells you how close a measurement is to the correct, accepted value. It is used in school and college science practicals, engineering tests, lab quality checks and anywhere a measured result is compared with a known standard. A small percentage error means an accurate measurement; a large one points to a problem with the method, the equipment or the reading.
How to use the calculator
- Enter the value you measured in your experiment.
- Enter the accepted, true or theoretical value from your textbook or reference.
- Read the percentage error, along with the absolute error, relative error and whether your value was too high or too low. The steps are shown for your lab report.
The formula
percentage error = |measured − accepted| ÷ |accepted| × 100
The vertical bars mean "absolute value", so the error is always positive. Some teachers use a signed version, without the absolute value on top, to show whether the result was above or below the true value; the "Direction" box gives you that information.
Worked example
A student measures the acceleration due to gravity with a pendulum and gets 9.62 m/s². The accepted value is 9.81 m/s².
- Absolute error = |9.62 − 9.81| = 0.19 m/s²
- Relative error = 0.19 ÷ 9.81 = 0.01937
- Percentage error = 0.01937 × 100 = 1.94%
The measurement is 1.94% too low, which is a good result for a simple school pendulum experiment.
Common sources of error
- Random errors: small, unpredictable changes, such as reaction time when starting a stopwatch. Reduce them by repeating the measurement and taking the average.
- Systematic errors: mistakes that push every result in the same direction, such as a balance that is not zeroed. Repeating does not remove them; you must fix the equipment or method.
- Reading errors: parallax when reading a scale at an angle.
Frequently asked questions
What is an acceptable percentage error?
It depends on the experiment. In many school practicals, under 5% is good. Precise lab work may require under 1%.
Is percentage error the same as percentage difference?
No. Percentage difference compares two measurements when neither is the true value, and divides by their average.
Can I calculate general percentages here?
For everyday percentages, use the Percentage Calculator.