Calculate percentage error between experimental and theoretical values, percentage difference between two values, or percentage change from one value to another.
Percentage error = |Experimental − Theoretical| / |Theoretical| × 100. It measures how close an experimental result is to the accepted value. A 0% error means perfect accuracy.
Acceptable error depends on the experiment. Physics experiments typically accept 1-5% error. Chemistry titrations aim for below 1%. Engineering tolerances vary from 0.001% (aerospace) to 10% (construction).
Percentage error compares a measured value to a known theoretical value. Percentage difference compares two measured values where neither is the reference. Use error when a true value is known; use difference when comparing two measurements.
Percentage change = (New − Old) / |Old| × 100. A positive result means increase; negative means decrease. Used for tracking price changes, growth rates, and experiment results over time.
Absolute error is the actual difference between measured and true values (same units as the measurement). Relative error is the absolute error divided by the true value (dimensionless). Relative error allows comparison across different scales.
Sources of error include instrument precision limits (systematic error), human reading errors (random error), environmental factors (temperature, pressure), and sampling bias. Recording errors and calculation mistakes also contribute.
Report both the measurement and its uncertainty: e.g. 9.8 ± 0.1 m/s². The uncertainty should match the precision of your instrument. Then calculate percentage error relative to the accepted value.