Percent Error Calculator

Calculate the percent error between a theoretical and experimental value, expressed as a percentage. The theoretical value is the expected value of measurement, while the experimental value is the actual value measured.
Theoretical Value:

Percent Error:

33.333%

Steps to Solve

Start with the percent error formula:
% error=|theoretical - experimental||theoretical|×100
Substitute values in the equation
% error=|75 - 100||75|×100
Simplify and solve
% error=2575×100
% error=0.33333333333333×100
% error=33.333333333333%


How to Calculate Percent Error

Percentage error is the margin of error in a measurement between the expected and actual values measured. It is used to express the difference between the expected and actual values in an experiment as a percentage.

Measuring percent error is important because it illustrates how close a measured or actual value is to the expected, theoretical value in an experiment. In chemistry it’s often used in tandem when measuring the percent yield of a reaction.

The expected value is sometimes called the theoretical, true, or accepted value. The actual value is sometimes referred to as the experimental value.

Graphic showing the percent error formula stating that % error is equal to the theoretical minus experimental divided by theoretical times 100%

Percent Error Formula

You can find the percentage error using the following formula:

error = |theoretical – experimental||theoretical| × 100%

Thus, percent error equals the absolute value of the theoretical value minus the experimental value, divided by the theoretical value, multiplied by 100%.[1]

To use the formula, start by subtracting the experimental value from the theoretical value to find the difference. Divide the difference by the theoretical value to find the relative error, then multiply by 100 to find the error as a percentage.

Our percent change calculator may also be useful for finding the amount of change between 2 values.

Example: Find the percent error between a theoretical value of 99 and experimental value of 98.


% error = |theoretical – experimental||theoretical| × 100%
% error = |99 – 98||99| × 100%
% error = 199 × 100%
% error = .010101 × 100%
% error = 1.01%

What is Percent Error

Because it is impossible to avoid measurement errors completely, there needs to be a way to define how much error there is when measuring.

Percent error is a measurement of the relative error between measurements in an experiment. It can tell you the precision, accuracy, or size of the error between measurements in an experiment.

Error Terminology

When conducting an experiment, the theoretical value is often referred to as the true value. This is the value expected to be seen when conducting a measurement.

The experimental value can also be called the observed value and is the value measured when conducting a measurement.

You might have also heard the term absolute error. Percent error is a little different.

Absolute error is the difference between the theoretical and experimental values.

absolute error = theoretical – experimental

Relative error is the difference between the theoretical and experimental values, divided by the theoretical value. Relative error is thus the amount of error relative to the whole.

relative error = theoretical – experimentaltheoretical

Standard error is a statistical measure of error based on the standard deviation of the results.

Now you can easily solve percentage error using the formula above or our handy calculator. Use our percentage calculators for more tools for calculating percent values.

References

  1. Wu, G., Baraldo, M., Furlanut, M., Calculating percentage prediction error: A user's note,
    Pharmacological Research
    , October 1995, 32(4), 241-248. https://doi.org/10.1016/S1043-6618(05)80029-5