Relative Error Calculator

Determining relative error involves two primary mathematical steps. First, you calculate the absolute error, which is the magnitude of the difference between the actual value and the measured value: Absolute Error = |Actual Value - Measured Value|. Second, you divide this absolute error by the absolute value of the actual value to yield a dimensionless fraction: Relative Error = Absolute Error / |Actual Value|. To express this result as a percentage, simply multiply the final fraction by 100%.

Imagine you are conducting a chemistry experiment where the theoretical or actual mass of a chemical compound is 50 grams, but your scale records a measured value of 47 grams. To find the relative error, you first determine the absolute error: |50 - 47| = 3 grams. Next, you divide this absolute error by the actual value: 3 / 50 = 0.06. Multiplying this decimal by 100% reveals a relative error of 6%, indicating a small but noticeable deviation in your measurement.

Always ensure your actual value and measured value share the exact same units before inputting them into the formula. Keep in mind that a small absolute error can sometimes translate to a large relative error if the actual value itself is very close to zero. Whenever possible, repeat measurements multiple times and average them to minimize random observational discrepancies.