Percent error or percentage error is a percentage of the variation between an estimate or measured value and an accurate or known value. It is employed in science to report the difference between a calculated or experimental value and a valid or actual value. Here is how to compute percent error, with an example, problem, calculation, and solution.

Summary: Percent Error

• A percent error calculation aims to gauge how close a measured value is to an actual value.
• Percent error is the disparity between the experimental and the theoretical value, divided by the theoretical value, multiplied by one hundred to give to yield percent.
• The percent error is always expressed as a positive number in some fields.
• Percent error is one kind of error calculation. Absolute and relative error are two other standard calculations. Percent error is part of a complete error analysis.
• The keys to correctly reporting percent error are knowing whether or not to drop the sign on the calculation and writing the value utilizing the correct number of significant figures.

The Formula

Percent error is the difference between a calculated or experimental value and an accepted or known value, divided by the recognized value, multiplied by 100%.

The percent error is always expressed as a positive value for many applications. Therefore, the absolute value of the error is divided by the accepted value and displayed as a percent.

|accepted value – experimental value| \ accepted value x 100%

It is customary for chemistry and other sciences to keep a negative value if one occurs. Whether error is positive or negative is crucial. For instance, you would not expect to yield a positive percent error equating actual to theoretical yield in a chemical reaction. On the other hand, if a positive value was computed, this would give clues as to problems with the procedure or unaccounted reactions.

When keeping the sign for error, the computation is the experimental or measured value less the known or the theoretical value, divided by the theoretical value and multiplied by 100%.

percent error = [experimental value – theoretical value] / theoretical value x 100%

Calculation Steps

1. Subtract one value from another. If you drop the sign (taking the absolute value), the order does not matter. Subtract the theoretical value from the experimental value if you keep negative symptoms. This value is your “error.”
2. Divide the error by the ideal value. This will yield a decimal number.
3. Translate the decimal number to a percentage by multiplying it by 100.
4. Add a percent or % symbol to illustrate your percent error value.

Example Problem, Calculation, and Solution

In a lab, you receive a block of aluminum. First, you measure the block’s dimensions and displacement in a container with a known volume of water. Next, you calculate the aluminum union’s density of 2.68 g/cm³. Then, you look up the thickness of a block of aluminum at room temperature and identify it as 2.70 g/cm³. Finally, calculate the percent error of your assessment.

1. Subtract one value from the other one: 2.68 – 2.70 = -0.02
2. You may discard any negative sign: 0.02. This is the error.
3. Divide the error by the actual value: 0.02/2.70 = 0.0074074
4. Multiply this number by 100% to get the percent error:
   0.0074074 x 100% = 0.74%. Considerable statistics are essential in science. If you report an answer employing too many or too few, it may be deemed incorrect, even if you set up the problem accurately.