Percent error
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01 // What it measures
Percent error compares a value you measured in a lab (the experimental value) to a known, accepted value (from a textbook, a reference table, or a more precise instrument). It tells you how far off your measurement was, as a percentage of the true value, so results with different units or sizes can still be compared fairly.
Percent error is always reported as a positive number — the formula uses absolute value, because being 5% too high and 5% too low are both a 5% error. If you need the direction of the error too, report it separately ("5% high").
02 // Worked example
A student measures the density of aluminum in a lab and gets 2.55 g/cm³. The accepted value is 2.70 g/cm³.
| Experimental value | 2.55 g/cm³ |
| Accepted value | 2.70 g/cm³ |
Formula percent error = |experimental − accepted| ÷ accepted × 100
03 // What counts as a good result
- In most middle and high school labs, under 5% error is considered good, and under 10% is usually acceptable for a hands-on measurement.
- Percent error is different from percent difference — percent difference compares two experimental values with no known "correct" answer, and divides by their average instead of an accepted value.
- A high percent error is not automatically a mistake. It is a signal to check your method: was a controlled variable off, was the tool read wrong, or was there a real limitation in the equipment?
04 // Choose the reference value carefully
Percent error answers how far an experimental result is from a designated accepted or reference value, relative to the size of that reference. Find the reference from a trusted source and confirm that it applies to the same material, conditions, units, and significant definition. A density value for pure copper at a stated temperature, for example, may not be an exact reference for an alloy or a warm sample. Record the source and conditions before calculating.
The reference value belongs in the denominator because it sets the scale for judging the difference. Keep the unrounded measured value and reference value through the calculation. If a question instead asks how two experimental groups differ, percent difference may be the intended calculation; that formula uses the average of the two results as the denominator. The labels are not interchangeable, so read whether there is one accepted target or two measurements being compared.
05 // Calculate, interpret, and report the result
Subtract the reference from the experimental value, take the absolute value, divide by the absolute reference, then multiply by 100 percent. The absolute value makes percent error a measure of size, not direction. Keep a separate signed difference if you also need to say whether the experiment produced a high or low result. A positive percent error alone does not tell the reader which direction the measurement went.
For example, a measured value of 9.6 units compared with a reference of 10.0 units gives an absolute difference of 0.4 units; 0.4 divided by 10.0 and multiplied by 100 is 4 percent. Explain that the result was 4 percent away from the reference and, separately, that it was below the reference. Include the original measurements and units in the report so the percentage does not hide the size of the underlying discrepancy.
06 // Understand what percent error cannot tell you
A small percent error does not prove that a method is accurate in every respect. The accepted value might be uncertain, the measurement may be rounded, or a systematic bias may have affected all trials. A large error can result from a unit conversion, instrument calibration, sample mix-up, or a genuine limitation of the procedure. Use the calculation as a clue for investigation rather than a grade for the experiment.
Percent error is undefined when the reference value is zero because division by zero is not possible. It can also behave strangely for reference values very close to zero, where a tiny absolute difference produces a very large percentage. In those cases report the absolute difference with units and explain why the relative comparison is unsuitable. Never change or discard data simply to make percent error look smaller.
07 // Use precision and uncertainty honestly
Round the final percentage only after using the available precision of the measurements. Reporting many decimal places implies a level of certainty the measuring tools may not support. A ruler marked only in millimeters cannot justify a result with six meaningful decimal places. Follow the class rule for significant figures, and retain a guard digit during intermediate steps to avoid rounding drift.
When repeated measurements are available, calculate percent error from the stated summary statistic—often the mean—unless the assignment specifies trial-by-trial comparisons. Report the spread or uncertainty alongside the mean when appropriate. Then compare the size of the error with that spread: a difference smaller than ordinary trial-to-trial variation may be difficult to distinguish, while a consistent offset across trials can point toward systematic error.
08 // Compare a set of trials fairly
If several trials estimate the same quantity, calculate the summary requested by the assignment, often the mean, and compare that value with the accepted reference. Also show the individual measurements or their spread. A mean can sit close to the reference even when the trials vary widely, so percent error alone does not describe repeatability.
Use percent error to discuss closeness to a reference, and use range, standard deviation, or measurement uncertainty to discuss variation when appropriate. Keep these ideas separate in the conclusion. A result may be precise but consistently offset, or less precise but centered near the reference; the next improvement depends on which pattern the data show.
09 // Questions people ask
Why is percent error always positive?
Because the formula takes the absolute value of the difference between your measurement and the accepted value, so a result that is too high and one that is too low by the same amount both give the same percent error.
What is a good percent error for a school lab?
There is no universal cutoff, but under 5% is usually considered a strong result, and under 10% is typically acceptable given the precision of school-grade equipment. Always check your teacher's rubric for the specific lab.
What is the difference between percent error and percent difference?
Percent error compares your result to a known, accepted value. Percent difference compares two experimental results to each other when there is no accepted value, dividing by the average of the two instead.