Percent Error Calculator

Percent error is defined as the absolute difference between the experimental and theoretical values, divided by the absolute value of the theoretical value, multiplied by 100. The formula is: Percent Error = |Experimental - Theoretical| / |Theoretical| * 100. The absolute value in the numerator ensures the result is always non-negative. Some conventions retain the sign to indicate whether the measurement was above (positive) or below (negative) the accepted value, but the most common convention uses the unsigned version. Percent error should not be confused with percent difference, which uses the average of the two values as the denominator. Percent error specifically uses the theoretical or accepted value as the reference, making it an asymmetric measure. This is appropriate when one value is established as the 'correct' answer. In laboratory settings, acceptable percent error varies by context. Introductory physics labs might accept errors up to 5-10%, while precision manufacturing might require errors below 0.01%. The context determines what constitutes a 'good' result. Sources of experimental error include systematic errors (instrument calibration, environmental conditions), random errors (reading fluctuations, noise), and human errors (parallax, rounding). Percent error quantifies the net effect of all error sources but does not identify their individual contributions. For that, error propagation analysis is needed. In quality control, percent error is used to determine whether products meet specifications. If a machined part should be 50.00 mm and the tolerance is 0.5%, any part measuring between 49.75 mm and 50.25 mm passes inspection. Percent error provides a scale-independent way to express tolerances that works across different measurement magnitudes.