Relative Error Formula

Relative error is calculated using the following formula using the actual values and measured values.

relative error formula

Relative Error Definition

Relative error is a measure of error in any given measurement with respect to the true value. For example if you have a chemical process that you know the theoretical yield from, but you measure a different value in the end, the difference between the two values is the relative error.


The following is a step by step example of calculating the relative error of an experiment.

  1. First, let’s set up the problem. Let’s say we are working on a chemical reaction that yields a certain amount of sugar as the results.
  2. Through theoretical chemistry, we know that the expected results should be that we end up with 20 grams of sugar. Instead we find a different value.
  3. After the experiment is done we determine that the process on yielded 10 grams of sugar.
  4. Finally, we should determine the relative error of this experiment. Using the true value of 20 grams and actual value of 10 grams, we find the relative error to be -100%.

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