Percent Error Calculator

The formula this calculator uses

percent error = |experimental - theoretical| / |theoretical| x 100

E

Experimental value, what you actually measured

T

Theoretical value, the accepted or true figure

|E - T|

Absolute error, the size of the gap ignoring direction

% error

The absolute error as a percentage of the accepted value

How to check the result by hand

1. 1

   Identify which value is the accepted one

   The accepted value is the denominator, so deciding which is which changes the answer. A known standard, a textbook constant or a certificate value is the accepted figure; your reading is the experimental one.

2. 2

   Subtract to find the absolute error

   Take the difference and drop the sign. Reading 105 against an accepted 100 gives 5, and reading 95 against 100 also gives 5, because both are equally far from the truth.

3. 3

   Divide by the accepted value

   Five divided by 100 is 0.05. This is the relative error, and it is the quantity to use if you are going to carry the number through further algebra.

4. 4

   Multiply by 100 for the percentage

   0.05 becomes 5 percent. The percentage is the version to report, because it is comparable across experiments with different units and different magnitudes.

5. 5

   Report the percent difference as well if there is no true value

   When comparing two measurements rather than a measurement against a standard, divide by the average of the two instead. For 105 and 100 that is 5 divided by 102.5, which gives 0.04878048780487805, slightly smaller than the percent error.