Percent Error Calculator
A percent error calculator helps determine how far an experimental or measured value is from an accepted or reference value. Percent error is commonly used in science, laboratory work, engineering, and mathematics to evaluate the accuracy of a measurement.
What Is Percent Error?
Percent error shows the difference between a measured value and an accepted value as a percentage of the accepted value. It focuses on the size of the error rather than simply giving the difference between two numbers.
Percent Error Formula
The standard formula is:
Percent Error = |Measured Value β Accepted Value| Γ· |Accepted Value| Γ 100%
The absolute value signs make the result positive because percent error normally describes the magnitude of the difference.
Percent Error Example
Suppose the accepted value is 50, but an experiment produces a measured value of 47.
Percent Error = |47 β 50| Γ· 50 Γ 100
= 3 Γ· 50 Γ 100 = 6%
The percent error is therefore 6%.
Another Example
If the accepted value is 200 grams and the measured value is 206 grams:
Percent Error = |206 β 200| Γ· 200 Γ 100
= 6 Γ· 200 Γ 100 = 3%
So, the measurement has a 3% percent error.
Percent Error vs. Percent Difference
Percent error and percent difference are related but are not used in exactly the same situation. Percent error compares a measured value with a known or accepted value. Percent difference is generally used when comparing two values without treating either one as the accepted reference.
Choosing the correct formula is important because the reference value determines how the error is calculated.
What Does a Percent Error Tell You?
A smaller percent error means the measured value is closer to the accepted value. A larger percent error indicates a greater difference between the measurement and the reference value.
A percent error of 0% means the measured value matches the accepted value exactly.
Where Is Percent Error Used?
Percent error is often used in laboratory experiments, physics, chemistry, engineering measurements, manufacturing, and other situations where measured results need to be compared with an accepted or theoretical value.
Common Mistakes to Avoid
Use the accepted value as the reference in the denominator. Do not accidentally divide by the measured value unless the specific method you are using calls for a different definition.
Also make sure both values use the same units before calculating the error. For example, do not compare kilograms directly with grams without converting one of the measurements first.
Quick Summary
Percent error measures the difference between a measured value and an accepted value relative to the accepted value. The basic formula is |Measured β Accepted| Γ· |Accepted| Γ 100%. It is a useful way to describe the accuracy of experimental and measured results.