Percent error tells you how far a measurement is from the value it should have. It’s a staple of science labs, where students measure something and compare it with the accepted figure.
It tells you whether you landed too high or too low, which a bare percentage doesn’t.
How to use the Percent Error Calculator#
- Enter your measurement. Type the value you measured.
- Enter the true value. Use the accepted or theoretical value.
- Read the percent error. The calculator shows the size and the direction of the error.
The formula#
Divide the gap between your measurement and the accepted value by the accepted value, then multiply by 100. The lab example below shows it with real numbers.
A worked lab example#
A student measures the acceleration due to gravity at 9.6 m/s² in a pendulum experiment. The accepted value is 9.81 m/s². The absolute error is |9.6 − 9.81| = 0.21. Dividing by the accepted value and multiplying by 100 gives a percent error of 2.14 percent. The signed version is negative, -2.14 percent, which shows the measurement was a little low.
Always divide by the accepted value, not the measured one, and keep the absolute error and percent error separate, since one has units and the other does not.
Percent error is not percent difference#
Absolute error is the plain gap between a measurement and the accepted value. Percent error scales that gap by the true value, so it only makes sense when you have a value you trust. Percent difference compares two measurements when neither is the standard, and it uses their average as the base. Percent change compares a before and an after. They look alike but answer different questions, and using the wrong one is a common cause of lost marks. If you only have two results and no true value, you want percent difference. For a change over time, use the percentage increase calculator.
What counts as a small error#
It depends on the field and the instrument. Teaching labs often accept 5 percent or less for simple measurements and ask students to explain larger errors. Precision engineering may allow only a fraction of a percent, and a pharmacist weighing a dose needs far tighter limits than someone measuring a room.
Look at what could cause the gap: instrument precision, reading errors, heat loss, air resistance or rounding. Repeating the measurement and averaging with our mean calculator usually reduces random error. A small percent error doesn’t prove a method is right, since a systematic bias can be small and still wrong in every trial. If the true value is zero, percent error is undefined because you can’t divide by zero. Report the absolute error instead.
Cutting your percent error#
Repeat the measurement several times and use the mean, which smooths random scatter. Use a more precise instrument, and read it at eye level. Calibrate against a known standard. Keep significant figures in line with your instrument, since an answer of 2.1374 from a ruler marked in millimetres claims precision you do not have. If every result is off in the same direction, you have a systematic error, such as a zero error on a scale or a timing delay, and no amount of repeating will fix it. Fix the method, not the average. For the average itself, use the mean calculator.
Frequently asked questions#
Subtract the true value from the measured value, take the absolute value, divide by the true value and multiply by 100.
The usual formula uses the absolute value, so it’s positive. The calculator also shows the signed version.
Percent error is undefined, because you can’t divide by zero.
The smaller the better. What counts as acceptable depends on the experiment.
Percent error = |measured − true| ÷ |true| × 100. You subtract the accepted value from your measurement, ignore the sign, divide by the accepted value and multiply by 100. If you want to know the direction too, keep the sign and say whether the measurement was above or below the true value.