Percent Error and Measurement Uncertainty: How to Judge a Result
October 21, 2026
Every measurement has some error. Percent error expresses how far a measured value is from the accepted or true value, relative to that value: percent error = |measured − accepted| ÷ accepted × 100. If a student measures the acceleration of gravity as 9.6 m/s² and the accepted value is 9.81 m/s², the error is |9.6 − 9.81| ÷ 9.81 × 100 = 2.14%.
Percent error is widely used in science labs, manufacturing, and quality control. Knowing how to compute and interpret it, and how to distinguish sources of error, helps you judge whether a result is good enough.
Skip the math and get your answer instantly:
Open the Percentage Calculator →Percent Error vs. Percent Difference
Use percent error when you compare an experimental value with a known reference. Use percent difference when comparing two measurements of equal standing, with neither considered the true value: |A − B| ÷ ((A + B) ÷ 2) × 100. If two thermometers read 20.4°C and 21.0°C, the percent difference is 0.6 ÷ 20.7 × 100 = 2.9%.
Be careful with temperature, because percent error depends on the scale's zero point. Use kelvin for meaningful percentages.
Accuracy and Precision
Accuracy describes how close measurements are to the true value. Precision describes how close repeated measurements are to each other. A scale that always reads 2 kg too high is precise but not accurate. A scale that gives widely varying readings centered on the true weight is accurate on average but not precise.
Percent error captures accuracy. The spread of repeated measurements, measured by the standard deviation, captures precision.
Systematic and Random Errors
Systematic errors push results consistently in one direction: a miscalibrated instrument, a zero offset, or a flawed method. They are not reduced by averaging, but by correcting the cause. Random errors scatter results in both directions because of small uncontrolled variations, such as reading a scale or reaction time with a stopwatch. Averaging many measurements reduces random errors by a factor of the square root of the number of measurements.
Taking 25 measurements instead of 1 cuts random error to one fifth of its single-measurement value.
| Error type | Cause | Fix |
|---|---|---|
| Systematic | Miscalibration, bias, flawed method | Calibrate, correct the method |
| Random | Small unpredictable variation | Repeat and average |
| Gross | Mistake, such as a misread dial | Recheck, discard if clearly wrong |
Combining Uncertainties
For sums and differences, add the absolute uncertainties (or in quadrature for independent errors). For products and quotients, add the relative (percent) uncertainties. If you measure a rectangle as 10.0 ± 0.1 cm by 5.0 ± 0.1 cm, the area is 50.0 cm² with relative uncertainty of about 1% + 2% = 3%, roughly ±1.5 cm². Measuring small quantities with the same absolute error gives larger percent error, so use larger quantities when you can.
Use significant figures to reflect the uncertainty: report 50 ± 2 cm², not 50.0000.
What Counts as Acceptable?
There is no universal threshold. A school lab might accept 5% to 10%, a machinist may require tolerances of 0.01%, and a pharmacist needs even tighter control. Define the acceptable tolerance before the measurement, based on the decision you need to make with it.
Frequently Asked Questions
What is the percent error formula?
|measured − accepted| ÷ accepted × 100.
What is the difference between accuracy and precision?
Accuracy is closeness to the true value. Precision is the consistency of repeated measurements.
How does averaging reduce error?
It reduces random error by about the square root of the number of measurements, but not systematic error.
How do I combine percent uncertainties in a product?
Add the relative uncertainties of the factors.
Is a lower percent error always better?
Yes, but it should be judged against the precision of the instruments and the purpose of the measurement.