How to Calculate Relative Error


Relative error is a number that compares how incorrect a quantity is from a number considered to be true. Unlike absolute error, where the error has the units of what is being measured, relative error is expressed as a percentage, defined as the absolute error divided by the true value. Read on to learn how to calculate relative error.

Things You'll Need

  • Paper and pen
  • Measurements to compute error for
  • Measuring device
  • To begin, a measurement has to take place: counting the money in a coin jar, measuring the length of a desk, so on and so forth. After determining what needs to be measured, the tool has to be determined. For counting coins, there is no real tool needed, but for measurements of length or temperature, then a tool is required. For example, to measure the long side of a sheet of letter paper, a ruler is used to measure the length. The measurement shows the paper length is 11.25 inches.

  • Error is a comparison between the measured value and true value. For the example, a sheet of letter paper is 8.5 inches times 11 inches. So the long side is 11 inches.

  • To compute the absolute error, the difference between measurement and the real value is taken. The example continues by the determination of the absolute error of .125 inches in the measurement.

  • The relative error is then computed by dividing the absolute error by the true value. In the example, .125inches/11inches yields a relative error of ~.011364.

  • To convert to percentage, multiply by 100. The relative error in the measurement in percent is 1.1364 percent.

Tips & Warnings

  • In a long process with many steps, computing the relative error at each step will identify those processes which can be improved.
  • Photo Credit folding ruler image by Scott McCarty from
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