How it works
Percent error measures how far a measured or observed value strays from its true (accepted) value, expressed as a percentage. It's widely used in laboratory work, engineering, and quality assurance to assess measurement accuracy and identify whether errors are systematic or random.
When you conduct an experiment or take a measurement, the result rarely matches the theoretical or reference value exactly. Percent error quantifies that gap in a standardized way, making it easy to compare accuracy across different scales and units.
The formula
Percent Error = |(Measured Value − True Value) / True Value| × 100
The vertical bars denote absolute value, which removes the sign and gives you the magnitude of error. Some applications keep the sign to show direction (whether the measurement was high or low).
Worked example
Suppose you're in a chemistry lab measuring the density of a metal sample.
- True (accepted) density: 8.96 g/cm³ (copper's known density)
- Your measured density: 8.70 g/cm³
Step 1: Find the difference.
8.70 − 8.96 = −0.26 g/cm³
Step 2: Divide by the true value.
−0.26 ÷ 8.96 = −0.02902
Step 3: Take the absolute value (remove the negative sign).
|−0.02902| = 0.02902
Step 4: Multiply by 100 to convert to percent.
0.02902 × 100 = 2.90% error
Your measurement was 2.90% lower than the accepted value. This is generally considered good accuracy for a lab experiment.
Another example with overestimation
Imagine measuring the boiling point of water.
- True value: 100 °C
- Measured value: 101.5 °C
Difference: 101.5 − 100 = 1.5 °C
Ratio: 1.5 ÷ 100 = 0.015
Percent error: 0.015 × 100 = 1.5% error
Here you overestimated by 1.5%, which is quite accurate for a thermometer reading.
Common mistakes
Forgetting the absolute value: Always use the absolute value unless you specifically need to track whether you over- or underestimated. Without it, a −5% error and a +5% error look different even though both represent the same magnitude of inaccuracy.
Using the wrong denominator: The true value always goes in the denominator. Using the measured value instead will give you a different (and incorrect) result. The true value is your reference standard.
Confusing percent error with significant figures: A 2.90% error is precise to three significant figures, but that doesn't mean your measurement itself has three significant figures. Report percent error appropriately, but don't assume it validates the precision of your raw data.
Ignoring context: A 10% error might be excellent in field geology but unacceptable in pharmaceutical manufacturing. Always evaluate error against the requirements of your specific application or experiment.