Percent Error Calculator
Calculate the percent error between a theoretical and observed value, expressed as a percentage. The theoretical value is the expected value of a measurement while the observed value is the actual value measured.
How to Calculate Percent Error
Percentage error is the margin of error in a measurement between the expected and actual values measured. Find percent error using the following formula:
Percentage Error Formula
Thus, percent error is equal to the theoretical value tv minus the observed value ov, divided by the theoretical value tv, multiplied by 100.
To use the formula, start by subtracting the observed value ov from the theoretical value tv 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 observed value of 98.
pe = ((tv – ov) ÷ tv) × 100
pe = ((99 – 98) ÷ 99) × 100
pe = (1 ÷ 99) × 100
pe = .010101 × 100
pe = 1.01%
What is Percent Error
Because it is impossible to completely avoid measurement errors 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.
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 observed value can also be called the experiment value and is the actually 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 observed values.
absolute error = tv – ov
Relative error is the difference between the theoretical and observed values, divided by the observed value. Relative error is thus the amount of error relative to the whole.
relative error = tv – ovtv
Percentage error is the relative error expressed as a percentage. This is why the result in the formula above is multiplied by 100.
percent error = tv – ovtv × 100
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 or our handy calculator. Use our percentage calculators for more tools for calculating percent values.