Percent Error Calculator
Find the percent error between a measured value and the accepted true value with the working shown, plus absolute, signed and relative error. Average several lab trials, check a tolerance, or work back from a percent error.
How it works
percent error = |measured − true| ÷ |true| × 100 · signed percent error = (measured − true) ÷ |true| × 100 · relative error = |measured − true| ÷ |true| · measured range = true × (1 ± p ÷ 100) · true value = measured ÷ (1 ± p ÷ 100)
Percent error measures how far a measured or estimated value falls from the accepted true value, scaled to the size of that true value. Take the absolute difference between the two, divide by the absolute true value, and multiply by 100. Because it divides by the true value, the same absolute miss counts as a larger error when the true value is small. Next to the percent error, the calculator shows the signed error, which tells you whether you overshot or undershot. It also gives the relative error as a decimal and the accuracy (100% minus the error). For lab work, choose several trials: the calculator averages them, gives the percent error of the mean and of each trial, and adds the standard deviation, a measure of precision. You can also work backwards, from a percent error to the range of readings it allows or to the true value behind a reading. Set an acceptable error limit under More options to get a pass or fail.
Worked example
A measurement reads 9.8 where the accepted value is 10. The error is 9.8 − 10 = −0.2, so the absolute error is 0.2. Dividing by 10 gives a relative error of 0.02, and the percent error is 2%: the reading is one part in fifty too low. If four trials read 9.7, 9.85, 9.9 and 9.75, their mean is 9.8, so the percent error of the mean is also 2%. The trials spread with a sample standard deviation of about 0.09. Working backwards, a 2% error around 10 allows readings from 9.8 to 10.2.
Sources: Approximation error — Wikipedia
Frequently asked questions
What does percent error tell me?
How far a measured or estimated value lands from the accepted true value, as a percentage of that true value. Smaller is better — a 2% error means the measurement is off by one part in fifty.
Should percent error ever be negative?
The standard definition uses the absolute difference, so it is never negative. Some teachers and textbooks keep the sign to show the direction. The calculator gives both: the signed percent error is negative when your measurement is below the true value and positive when it is above.
What’s the difference between percent error and percent difference?
Percent error compares a measurement against a known correct value. Percent difference compares two measurements when neither is the accepted truth, dividing by their average instead.
How do I find the percent error of several trials?
Average the trials first, then compare the mean with the true value. Choose “Percent error of several trials” and list your readings. You also get each trial’s own percent error and the average of those errors. The standard deviation shows how consistent the trials were.
What is the difference between accuracy and precision?
Accuracy is how close your results are to the true value, which percent error measures. Precision is how close your results are to each other, which the standard deviation measures. A set of trials can be precise but inaccurate if they cluster tightly around the wrong value.
What is an acceptable percent error?
It depends on the experiment and the instrument. In school labs, under 5% is often considered good and up to 10% acceptable, while calibrated lab equipment may be held to a fraction of a percent. Enter your limit under More options to get a pass or fail.
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This calculator is for educational purposes. Double-check important results before acting on them.