Calculate the percent error between an experimental (measured) value and a theoretical (accepted) value. Used in science labs and statistical analysis.
Percent Error = |Experimental − Theoretical| / |Theoretical| × 100
Absolute Error = |Experimental − Theoretical|
Relative Error = |Experimental − Theoretical| / |Theoretical|
Signed Percent Error = (Experimental − Theoretical) / |Theoretical| × 100
A positive signed error means the experimental value was higher than expected (overestimate). A negative signed error means it was lower (underestimate). Smaller percent error = more accurate measurement.
A "good" percent error depends on the experiment's precision requirements. In many high school and college lab settings, a percent error under 5% is considered acceptable. For highly precise physics or chemistry experiments, under 1% may be required. For rough engineering estimates, up to 10% might be fine. The key is that the percent error should be consistent with the precision of your measuring instruments and method.
Yes, percent error can exceed 100%. This occurs when the absolute difference between your experimental and theoretical values is larger than the theoretical value itself. For example, if the theoretical value is 5 and your measurement is 12, the error is |12−5|/|5| × 100 = 140%. A percent error over 100% usually indicates a significant problem with the experimental method or measurement technique.
It expresses how far an experimental result sits from the accepted or true value, as a proportion of that true value.
The denominator is the actual value, not the measured one. The absolute value bars mean the result is normally reported as a positive figure regardless of direction.
Measuring the density of aluminium as 2.60 g/cm³ against an accepted 2.70:
(|2.60 − 2.70| ÷ 2.70) × 100 = (0.10 ÷ 2.70) × 100 = 3.7%
These are distinct, and percent error only measures one of them.
A badly calibrated instrument can be highly precise and badly inaccurate: five readings clustered tightly together, all wrong by the same amount. Precision alone is no evidence of correctness.
What counts as acceptable depends entirely on context. A school experiment within 5% is usually fine. Analytical chemistry or engineering tolerances may require a fraction of a percent.
Repeating a measurement helps with random error and does nothing for systematic error — which is why a consistently wrong result points to method or equipment rather than carelessness.