What percent error tells you
Percent error measures how far a measured or estimated value is from an accepted, true or theoretical value, as a percentage of that accepted value. It is used in school and university science labs, quality control, surveying and forecasting to judge how accurate a result is. A small percent error means the measurement is close to the reference value.
The formula
Percent error = |measured − accepted| ÷ |accepted| × 100
The vertical bars mean "absolute value": drop any minus sign. Most textbooks report percent error as a positive number. If you also want to know the direction, use the signed version without the bars in the top line: a positive result means the measurement was too high, a negative result means it was too low. The calculator shows both.
Worked examples
1. Measuring gravity with a pendulum
A class measures the acceleration due to gravity as 9.6 m/s². The accepted value near the Earth's surface is about 9.81 m/s².
|9.6 − 9.81| ÷ 9.81 × 100 = 0.21 ÷ 9.81 × 100 = 2.14%. The measurement is 2.14% too low.
2. Boiling point of water
A thermometer reads 98.5 °C in boiling water where the expected value is 100 °C. |98.5 − 100| ÷ 100 × 100 = 1.5%. (At high altitude water really does boil below 100 °C, so check which accepted value applies.)
3. Weighing a reference mass
A kitchen scale shows 152 g for a 150 g calibration weight. |152 − 150| ÷ 150 × 100 = 1.33% too high.
Absolute, relative and percent error
| Measure | Formula | Gravity example |
|---|---|---|
| Absolute error | |measured − accepted| | 0.21 m/s² |
| Relative error | absolute error ÷ |accepted| | 0.0214 |
| Percent error | relative error × 100 | 2.14% |
Absolute error keeps the units of the measurement, which is useful when comparing results on the same scale. Relative and percent error have no units, so you can compare the accuracy of very different measurements, such as a length in millimetres and a mass in kilograms.
Percent error vs percent difference
Percent error needs a known reference value. When you compare two measurements and neither is the "true" one, for example two students' results or two instruments, use percent difference instead:
Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100
For 9.6 and 9.7: 0.1 ÷ 9.65 × 100 = 1.04%. Percent change is a third, different idea: it compares a new value with an old one. The percentage calculator covers percent change.
What counts as a good percent error?
It depends entirely on the task. In many introductory physics and chemistry labs, results within about 5% are often considered reasonable, and within 1–2% good, but your instructor's guidance comes first. Industrial and medical measurements can require far tighter tolerances, while rough estimates may accept 10% or more. Percent error should always be read alongside the uncertainty of the measurement: a 2% error is fine if your instruments are only accurate to ±3%.
Accuracy and precision
Percent error measures accuracy: how close a result is to the true value. Precision is how close repeated measurements are to each other. A set of results can be precise but inaccurate (all close together but off target, often a sign of a systematic error such as a badly zeroed scale) or accurate on average but imprecise (scattered around the right value). Take several readings, find their mean with the average calculator, and compute the percent error of the mean.
Common sources of error in experiments
- Systematic errors push every result the same way: an uncalibrated instrument, reading a scale from an angle (parallax), heat lost to the surroundings.
- Random errors scatter results both ways: reaction time with a stopwatch, small fluctuations in readings.
- Using the wrong accepted value, for example 100 °C for boiling water at altitude, or standard gravity (9.80665 m/s²) when local gravity differs slightly.
- Rounding too early in intermediate steps of the calculation.
Common mistakes
- Dividing by the measured value instead of the accepted value.
- Forgetting to multiply by 100, giving 0.0214 instead of 2.14%.
- Using percent error when there is no true value; use percent difference instead.
- Accepted value of zero: percent error is undefined, because you would divide by zero. Report the absolute error instead.
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100. For a measured 9.6 and accepted 9.81, it is 0.21 ÷ 9.81 × 100 = 2.14%.
Can percent error be negative?
Usually it is reported as a positive number using absolute value. A signed percent error keeps the sign: negative means the measurement was too low, positive means too high.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value. Percent difference compares two values when neither is the reference, dividing by their average.
What is an acceptable percent error?
It depends on the field and the instruments. In many introductory labs, under about 5% is considered reasonable, but follow your instructor's or industry's tolerance.
Why is percent error undefined when the true value is zero?
The formula divides by the accepted value, and division by zero is undefined. In that case report the absolute error in the measurement's units.
Sources
- NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results.
- 3rd General Conference on Weights and Measures (CGPM, 1901): standard acceleration of gravity 9.80665 m/s².
- Joint Committee for Guides in Metrology, JCGM 200:2012 International Vocabulary of Metrology (accuracy, precision, measurement error).
Last reviewed 15 October 2026. Results are estimates; see our disclaimer.