⚠ Percent Error Calculator
Percent error measures how far a measurement sits from the value it should have been. It is the standard way of reporting accuracy in a lab report, and it is reported as an absolute figure unless the direction matters.
Measuring how far off a measurement was
Percent error compares what you measured against what the value should have been, expressed as a proportion of the accepted value. It is the standard way of reporting accuracy in a lab report, and it answers a different question from precision, which is about repeatability.
percent error = |measured − accepted| / |accepted| × 100
Always divide by the accepted value
The denominator is the known or theoretical value, never the measured one. Dividing by the measurement makes the error depend on how wrong you were, which produces a different answer depending on the direction of the mistake and is not comparable between experiments. Measuring 9.65 against an accepted 9.81 gives 1.63%; dividing by 9.65 instead would give 1.66%, and the gap widens as the error grows.
Accuracy and precision are different
| Accurate | Not accurate | |
|---|---|---|
| Precise | Tight cluster on the true value — the goal | Tight cluster in the wrong place — systematic error |
| Not precise | Scattered around the true value — random error | Scattered and off-centre — both problems |
Percent error measures accuracy. The standard deviation of repeated measurements measures precision. A set of readings that are tightly clustered but all 5% high points at a calibration problem; readings scattered around the right answer point at random noise. The two have completely different fixes.
What counts as acceptable
| Percent error | Typical reading |
|---|---|
| Under 1% | Excellent for school and undergraduate work |
| 1–5% | Normal for careful work with simple equipment |
| 5–10% | Suggests a systematic issue worth identifying |
| Over 10% | Usually a method or arithmetic problem, not random error |
Context matters enormously. A 2% error measuring gravity with a pendulum in a school lab is a good result; a 2% error in a pharmaceutical assay is a failed batch. Analytical chemistry often works to 0.1%, while field measurements in ecology might accept 20%.
The sign is information
The absolute value is what gets reported, but the signed error tells you something the magnitude does not. A consistently positive error across repeated trials means you are systematically overestimating: a miscalibrated instrument, a parallax reading error, an unaccounted-for force. Random error produces signs that scatter. If every one of your trials errs in the same direction, the cause is systematic and findable.
This is why lab reports should record the signed errors even when reporting the absolute figure. Five trials all reading 3% high is a much more useful finding than an average error of 3%.
Percent error against percent difference
Percent error needs an accepted value. When you are comparing two measurements and neither is authoritative, use percent difference instead, which divides by the average of the two:
percent difference = |a − b| / ((a + b)/2) × 100
Comparing two students' results, or two instruments, calls for percent difference. Comparing a result against a textbook constant calls for percent error.
A worked example
A pendulum experiment measures gravitational acceleration as 9.65 m/s² against an accepted 9.81. The absolute error is 0.16, the percent error is 1.63%, and the accuracy is 98.37%. The sign is negative, so the measurement is low. If all five trials came out low, the likely causes are a consistently over-measured string length or timing that started late, both of which produce a systematic underestimate.
The natural follow-ups are the percentage calculator, for what this figure feeds into, and the standard deviation calculator, for the closely related case.
Frequently Asked Questions (FAQs)
What is the formula for percent error?
The absolute difference between the measured and accepted values, divided by the accepted value, times 100. The denominator is always the accepted or theoretical value, never the measurement.
Can percent error be negative?
The reported figure is conventionally absolute, so no. The signed version is still useful internally: a consistent sign across trials indicates systematic error, while scattered signs indicate random error. Report the absolute value and discuss the sign.
What is a good percent error?
Under 5% is normal for careful work with school or undergraduate equipment, and under 1% is excellent. What counts as acceptable depends entirely on the field: analytical chemistry expects 0.1%, field ecology might accept 20%.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known accepted value and divides by that value. Percent difference compares two measurements where neither is authoritative and divides by their average. Use the second when there is no textbook answer.
Why is my percent error so high?
Most often a systematic cause: an uncalibrated instrument, a unit conversion mistake, an unaccounted-for variable, or an arithmetic slip. Errors above 10% are rarely random noise. Check the units first, which is the single most common culprit.
What if the accepted value is zero?
Percent error is undefined, because you would be dividing by zero. Report the absolute error instead, or use percent difference against a meaningful reference. This comes up with measurements of net force or temperature difference that should theoretically be nil.