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.
Percentages express a number as a fraction of 100. They're used everywhere: discounts, tax rates, tip amounts, grade scores, growth rates, and financial returns. The key is knowing which type of percentage you're calculating — percentage of a value, percentage change, or percentage difference — because each uses a different formula.
Percentage increase vs. percentage points: A rate going from 5% to 8% is a 3 percentage point increase, but a 60% percentage increase. These are not the same thing, and confusing them is extremely common in news coverage.
Percentage off vs. percentage of original: "30% off $200" = $140 (you pay 70% of $200). "Pay 30% of $200" = $60. Read the phrasing carefully.