Experimental against accepted value: absolute error, percent error and every step. Runs on your device.
Each row uses the formula above with the usual school accepted value. Error is measured minus accepted, so a minus means the measurement was low.
| Quantity | Accepted | Measured | Error | Percent error |
|---|---|---|---|---|
| Density of water (g/mL) | 1 | 0.97 | -0.03 | 3% |
| Gravity g (m/s2) | 9.81 | 9.6 | -0.21 | 2.14% |
| Boiling point of water (C) | 100 | 98.5 | -1.5 | 1.5% |
| Speed of sound at 20 C (m/s) | 343 | 335 | -8 | 2.33% |
Accepted values: water 1.00 g/mL near 4 C, standard gravity rounded to 9.81, water boiling at 100 C at 1 atm, sound in dry air at 20 C about 343 m/s. Percent error shown to 2 decimals.
The three look alike but answer different questions. The example row for each uses the numbers 80 and 100.
| Measure | Formula | Use it when | Example |
|---|---|---|---|
| Percent error | |measured − accepted| ÷ |accepted| × 100 | You measured something and know the true or accepted value | Accepted 80, measured 100: 25% |
| Percent difference | |A − B| ÷ ((A + B) ÷ 2) × 100 | You compare two values and neither is the reference | 80 and 100: 22.22% |
| Percent change | (new − old) ÷ |old| × 100 | One value moved over time, such as a price or a population | 80 to 100: +25% |
Percent error and percent change share a formula shape, but percent error treats the second number as a measurement of the first.
Percent error is the size of your measurement error as a percentage of the accepted value: |experimental − accepted| ÷ |accepted| × 100. If a lab says g is 9.81 m/s² and you measured 9.6, the error is 9.6 − 9.81 = −0.21, the absolute error is 0.21 and the percent error is 0.21 ÷ 9.81 × 100 = 2.14%. The page opens on that example and writes the substituted formula line by line, so you can copy the steps into a lab report. The accepted value is the one you trust, such as a textbook constant or a theoretical yield. The experimental value is what you measured or calculated.
Most school courses define percent error with the absolute value, so the answer is never negative. Some labs keep the sign instead, to show whether the measurement came out over or under the accepted value. This page shows both: Percent error is the absolute form, and Signed percent error keeps the plus or minus. A plus means your value was above the accepted one and a minus means it was below. Check your lab manual, because a teacher who asks for the signed form will mark an unsigned answer down. Absolute error is a different number: it is the plain size of the error in the units of the measurement, here 0.21 m/s², not a percentage.
Turn on Several trials to enter up to 8 measured values against one accepted value. The table gives each trial's error and percent error. The headline is the mean percent error, the average of the trial percent errors. A second number, Percent error of the mean value, averages your measurements first and then compares that mean with the accepted value. They differ when trials fall on both sides of the accepted value: errors of +2% and −2% have a mean percent error of 2%, but the mean value can sit on the accepted value and give 0%. Ask which one your instructor wants.
Percent error divides by the accepted value, so an accepted value of 0 has no percent error. A freezing point set at 0 °C is the common case in school labs. The page shows a message instead of a number. Report the absolute error, or restate the measurement on a scale with a non-zero reference, such as kelvin. Percent error is also not percent difference or percent change, which answer other questions and are compared in the table below. The Percentage Calculator covers those. Results come only from the numbers you type, and the accepted values in the examples are the usual school figures, not a data source.
Percent error = |experimental − accepted| ÷ |accepted| × 100. With an accepted density of 1.00 g/mL and a measured 0.97 g/mL, the error is 0.03, and 0.03 ÷ 1.00 × 100 = 3%. The page writes each substituted step under the answer.
Not in the usual school definition, which takes the absolute value. If your course keeps the sign, use Signed percent error: a boiling point of 98.5 against 100 gives −1.5%, meaning the measurement was low. A sign tells you the direction, not how good the result is.
Percent error is undefined, because it divides by the accepted value. A freezing point of 0 °C is the typical case. Report the absolute error, for example 0.4 °C, or ask your teacher which measure to use.
It depends on the instrument and the course. Under 5% is often considered acceptable in an introductory lab, and under 1% good, but those are rules of thumb. Your syllabus or lab rubric sets the limit.
No. Mean percent error averages each trial's percent error. The percent error of the mean averages your measurements first. Trials of 9.4 and 10.2 against 9.81 give a mean percent error of 4.08%, but their mean 9.8 gives only 0.1%.
Percent error compares a measurement with a known accepted value. Percent difference compares two values with no reference, using their average as the base: 80 and 100 differ by 22.22%. Use the table above on this page to pick the right one.