In the fields of science and engineering, accurate measurements and calculations are of utmost importance. As part of this process, assessing the reliability of experimental results is essential. One such measure is the relative error, which helps determine the accuracy of a value based on its deviation from the true value. In this article, we will provide a step-by-step guide on how to calculate relative error.
Relative error is a measure that compares the difference between an estimated or measured value (approximate value) and an accepted or exact value (true value), relative to the true value. It is generally expressed as a percentage and is used to determine how inaccurate measurements are with respect to their accuracy.

Follow these steps to calculate relative error:

1. Determine the True Value: The true value refers to the exact or accepted value of a measurement or calculation in the problem at hand. This could be based on standardized measurements or confirmed findings.

2. Determine the Approximate Value: The approximate value corresponds to the measured or calculated outcome generated during an experiment or test.

3. Find the Absolute Error: To find the absolute error, subtract the approximate value from the true value (or vice versa) and disregard any negative sign that may arise as a result.

Absolute Error = |True Value – Approximate Value|

4. Calculate Relative Error: The relative error can now be calculated by dividing the absolute error by the true value and multiplying by 100 to express it as a percentage.

Relative Error = (Absolute Error / True Value) x 100%

Let’s calculate relative error using an example:

Suppose you measure the length of a table using a ruler and get a measurement of 120 cm, while its known or true length is 125 cm.

1. True Value = 125 cm

2. Approximate Value = 120 cm

3. Calculate Absolute Error:

Absolute Error = |125 – 120| = 5 cm

4. Calculate Relative Error:

Relative Error = (5 / 125) x 100% = 4%

In this example, the relative error in measuring the length of the table is 4%.

In conclusion, calculating relative error helps determine the accuracy of experimental results or measurements. It provides insight into the level of precision in a given measurement and helps identify potential sources of error in experiments. By following the step-by-step guide provided above, you can successfully calculate the relative error for your measurements and have a clear understanding of their accuracy.