Percent Error Calculator
How far a measurement is from the accepted value — with the working shown.
Percent error
This is the last answer worked out. Fix the input above to update it.
The accepted value is 0, so the percent error is undefined: it divides by the accepted value. Use the absolute error, or compare the values with the percentage difference.
Trials
| Trial | Measured | Error | Percent error |
|---|
Working
About the Percent Error Calculator
Percent error tells you how far a measurement is from the accepted (true, theoretical or reference) value, as a percentage of that value. Type your measured value and the accepted value to get the percent error, the absolute error and the relative error, with every step of the working filled in. Show the percent error as an absolute value — its size, always positive, as most lab reports ask — or signed, so that + means the measurement was too high and − too low.
With several trials, type them all: you get each trial’s error in a table, the mean and its percent error, the mean absolute error, the mean absolute percent error and the standard deviation of the trials, so you can discuss both accuracy and precision. The arithmetic is exact, so the only rounding is to the decimal places you choose.
How to use it
- Type the measured (experimental) value — or several trials, one per line or separated by spaces or commas (a row pasted from a spreadsheet, such as
9.78,9.82,9.75, works too). - Type the accepted value and, if you like, a unit (it is only used as a label).
- Choose the number of decimal places and whether the percent error is shown as absolute or signed.
- Read the result and the working. Copy them, or download the trials as a CSV file.
Examples
Measured 9.6 m/s², accepted 9.81 m/s²
2.14% (signed −2.14%)
|9.6 − 9.81| ÷ 9.81 × 100% = 0.21 ÷ 9.81 × 100% ≈ 2.14%.
Measured 105, accepted 100
5.00% (signed +5.00%)
Measured 98.6 °C, accepted 100 °C
1.40%
A Celsius temperature has an arbitrary zero, so its percent error depends on the scale; in kelvin the same error is 1.4 ÷ 373.15 ≈ 0.38%.
9.78, 9.82 and 9.75 m/s², accepted 9.81 m/s²
Mean 9.783 m/s², 0.27% low
The trials themselves are 0.31% low, 0.10% high and 0.61% low; their mean absolute percent error is 0.34%.
Common uses
- Lab reports in physics and chemistry: comparing a measured constant with its textbook value.
- Checking how accurate an instrument or a method is against a reference value.
- Comparing several trials: accuracy (percent error of the mean) against precision (their spread).
The formulas
- Error = measured − accepted. This is the measurement error of the International Vocabulary of Metrology (VIM 2.16): positive when the measurement is too high.
- Absolute error = |measured − accepted|, in the unit of the measurement.
- Relative error = absolute error ÷ |accepted value|, a plain number.
- Percent error = relative error × 100%.
- Signed percent error = (measured − accepted) ÷ |accepted value| × 100%.
Accuracy, precision and several trials
Percent error measures accuracy — how close you are to the accepted value. Repeating the measurement shows precision — how close the trials are to each other — which the sample standard deviation (dividing by n − 1) describes.
With several trials the percent error of the mean can be much smaller than the trials’ own errors, because errors above and below the accepted value cancel in the mean. The mean absolute percent error averages the sizes of the errors without letting them cancel, so it is never smaller than the percent error of the mean. Report the one your course asks for, and say which it is.
Percent error, percentage difference or percentage change?
Use percent error when one value is known to be right, such as a textbook constant or a certified reference value. When you compare two measurements and neither is the true value, use the percentage difference, |a − b| ÷ ((|a| + |b|) ÷ 2) × 100%, which divides by their average; the calculator shows it too, and the percentage calculator works it out for any two numbers. Percentage change, (new − old) ÷ |old| × 100%, is for a value that changed from one number to another.
Limitations
- The accepted value cannot be 0, because percent error divides by it; the absolute error and the percentage difference are still shown.
- For quantities with an arbitrary zero, such as temperatures in °C or °F, percent error depends on the scale; use kelvin, or report the absolute error.
- Percent error describes accuracy only. It is not a measurement uncertainty and does not replace an uncertainty analysis.
- Up to 500 trials, with up to 60 digits in each number. The unit is only a label and is not converted.
Privacy
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Frequently asked questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100%. For a measured 9.6 m/s² against 9.81 m/s²: |9.6 − 9.81| ÷ 9.81 × 100% = 0.21 ÷ 9.81 × 100% ≈ 2.14%.
Can percent error be negative?
Only if you keep the sign. The usual percent error uses the absolute value and is never negative. The signed version, (measured − accepted) ÷ |accepted| × 100%, is negative when the measurement is too low and positive when it is too high. Choose Signed ± to show it.
What is a good percent error?
There is no fixed threshold — it depends on the experiment and the instruments. A few percent can be very good for a school pendulum experiment and far too much for a calibrated balance. Compare the error with the uncertainty of your measurements and with what your course or method expects.
What is the difference between absolute error and relative error?
Absolute error is the size of the error in the unit of the measurement (0.21 m/s²). Relative error divides it by the accepted value (0.21 ÷ 9.81 ≈ 0.0214) and has no unit, so errors in different quantities can be compared. Percent error is the relative error × 100%.
How do I work out percent error for several trials?
Usually you average the trials first and work out the percent error of the mean. Some courses instead ask for the average of the trials’ percent errors (the mean absolute percent error). Type all the trials and the calculator gives both, together with each trial’s own error.