How to Calculate Percent of Error

An absolute error is the different between an approximate (measured) value and exact (true) one. But, an error of 1 pound when you weigh an object of true mass 5 pounds versus one of 100 pounds is a far higher percent of error. Percent of error reports on the ratio (in percents) between the absolute error and the true value.
As an example, let's calculate the percent of error if you measured the height of a desk and obtain a value of 39 inches while the correct length has turned to be 41 inches.

Things You'll Need

• Calculator

Instructions

1. Calculate the difference (the absolute error) between the measured and true value.
   Difference = measured value-true value
   In our example, Difference = 39 inches---41 inches = ---2 inches.

2. Obtain the absolute value (modulus) of the difference from Step 1 using the following rules:
   |difference| = difference, if difference ≥ 0.
   |difference| = -1 x difference, if difference ˂ 0.
   Note: "| |" is a modulus sign.
   In our example, |difference| = ---1 x (---2 inches) = 2 inches, since ---2 ˂ 0.

3. Obtain the ratio (the relative error) between the difference modulus and the true value.
   Relative error = |difference|/true value.
   In our example, Relative error = 2 inches/41 inches = 0.0488.

4. Obtain percent of error.
   Percent of error = Relative error x 100%.
   In our example, Percent of error = 0.0488 x 100% = 4.88%.

References

• "Lab Math: A Handbook of Measurements, Calculations, and Other Quantitative Skills for Use at the Bench", D.S. Adams, Cold Spring Harbor Laboratory Press, Sep. 1, 2003.