Percent Error Calculator
Type your measured value and the accepted (true) value to get the percent error, the absolute and relative error and whether you were too high or too low. Percent difference compares two results when neither is the right one. Advanced adds several trials with the mean, standard deviation and each trial’s error.
Use this when neither value is known to be right, like two students’ results or two instruments.
Separate them with commas, spaces or new lines. You can paste a column from a spreadsheet.
Percent error has no unit, but both values must be in the same unit. Convert one first if they are not (for example g and kg).
How your percent error is worked out
Your numbers, step by step: the gap, drop the sign, divide by the accepted value, then × 100.
- 1
Find the gap
9.65 − 9.81 = −0.16
- 2
Drop the sign
|−0.16| = 0.16
- 3
Divide by accepted
0.16 ÷ 9.81 = 0.0163
- 4
Times 100
0.0163 × 100 = 1.63%
Read more: the formula, a worked example, percent difference vs change, and accuracy vs precision
Percent error tells you how far a measurement is from the accepted (true, theoretical or textbook) value, as a percentage of that accepted value. It is the standard way to report how accurate a lab result is, and it works the same in any unit, as long as both numbers are in the same one.
The formula
absolute error = |measured − accepted|
relative error = absolute error ÷ |accepted|
percent error = |measured − accepted| ÷ |accepted| × 100
signed percent error = (measured − accepted) ÷ |accepted| × 100 (+ too high, − too low)
percent difference = |a − b| ÷ (|a + b| ÷ 2) × 100
percent change = (new − old) ÷ |old| × 100
Worked example
A pendulum experiment gives g = 9.65 m/s². The accepted value is 9.81 m/s².
- The gap: 9.65 − 9.81 = −0.16 m/s². The minus sign means the measurement is too low.
- Absolute error: |−0.16| = 0.16 m/s².
- Relative error: 0.16 ÷ 9.81 = 0.016310 (to 6 decimal places).
- Percent error: 0.016310 × 100 = 1.63% (to 2 decimal places). Signed, it is −1.63%.
- The measurement is 9.65 ÷ 9.81 = 98.37% of the accepted value.
Several trials. Five trials give 9.72, 9.65, 9.91, 9.78 and 9.69 m/s². Their sum is 48.75, so the mean is 48.75 ÷ 5 = 9.75 m/s². The mean is 0.06 below 9.81, so the percent error of the mean is 0.06 ÷ 9.81 × 100 = 0.61%. Each trial’s error is −0.09, −0.16, +0.10, −0.03 and −0.12, so the mean absolute error is 0.50 ÷ 5 = 0.10 m/s². The deviations from the mean square to 0.0009, 0.01, 0.0256, 0.0009 and 0.0036, which add to 0.041. Dividing by 5 − 1 = 4 gives 0.01025, and its square root is the sample standard deviation, 0.101 m/s².
Percent difference. Two groups measure 48 g and 52 g. The gap is 4 g and the average is (48 + 52) ÷ 2 = 50 g, so the percent difference is 4 ÷ 50 × 100 = 8%. As a percent change, 48 → 52 is 4 ÷ 48 = +8.33%, and 52 → 48 is −4 ÷ 52 = −7.69%.
Which one should I use?
| Use | When | Divide by |
|---|---|---|
| Percent error | You know the true value (a textbook constant, a known mass, a calculated answer) | The accepted value |
| Percent difference | Two results, neither known to be right (two students, two methods) | The average of the two |
| Percent change | A value that moved from old to new (a price, a reading over time) | The old value |
Accuracy vs precision
Accuracy is how close your results are to the true value: a small percent error (of the mean) means accurate. Precision is how close your results are to each other: a small standard deviation or relative standard deviation means precise. You can be precise but not accurate (all your darts land close together, but away from the bullseye), which usually points to a systematic error such as a badly zeroed balance. Random errors spread the results out and hurt precision; averaging more trials reduces their effect on the mean.
Notes
- Negative values (temperatures in °C, charges, displacements) work: the calculator divides by the size of the accepted value, so the error is never flipped by its sign.
- An accepted value of 0 has no percent error, because you cannot divide by 0. The absolute error is still shown.
- Units: °C and °F readings near 0 give huge percent errors that mean little; use kelvin, or report the absolute error, for temperatures.
- Sample or population SD: lab trials are a sample, so the sample standard deviation (dividing by n − 1) is the usual choice. The population figure is shown too.
- How many decimal places? Two is usual for percent error. Match your absolute error to the precision of your measurements.
Common questions
What is the formula for percent error?
Percent error = |measured value − accepted value| ÷ |accepted value| × 100. Take the gap between your result and the true value, drop the minus sign, divide by the true value and multiply by 100. Measuring g as 9.65 m/s² when it is 9.81 m/s² gives 0.16 ÷ 9.81 × 100 = 1.63%.
Can percent error be negative?
The usual percent error is always positive because it uses the size of the gap. Some teachers and textbooks ask for the signed version, (measured − accepted) ÷ accepted × 100, where a minus sign means your result was too low and a plus sign means too high. Advanced lets you show either.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value, so you divide by the true value. Percent difference compares two values when neither is known to be right, like two students’ results, so you divide by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. Percent change is for a value that moved from an old number to a new one, so you divide by the old number.
What is a good percent error?
It depends on the experiment and the equipment. In many school labs, under 5% counts as good and under 1% as very good, but a careful measurement with precise instruments can expect much less, and a rough estimate much more. Compare your error with the uncertainty of your equipment.
What if the accepted value is 0?
Then percent error cannot be worked out, because you cannot divide by 0. Report the absolute error (how far off you were, in your units) instead, or use percent difference if you are comparing two measurements.
How do I find percent error with several trials?
Usually you average the trials first and find the percent error of the mean: for 9.72, 9.65, 9.91, 9.78 and 9.69 m/s² the mean is 9.75, so the error is 0.06 ÷ 9.81 × 100 = 0.61%. The standard deviation (0.10 m/s² here) shows how precise the trials were. Some teachers instead want the percent error of each trial, or their average; Advanced shows all of them.
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