Definition of percentage error
Percent error, is an expression of the difference between a measured value and the known or accepted value. It is often used in science to report the difference between experimental values and expected values.
Note: Sometimes it is useful to know whether the error is positive or negative. If you need to know the positive or negative error, this is done by removing the absolute value brackets in the formula. In most cases, the absolute error is fine. For example, in experiments involving yields in chemical reactions, you are unlikely to get more product than is theoretically possible.
Steps to calculate the percentage error
- Subtract the accepted value from the experimental value.
- Take the absolute value from step 1
- Divide that answer by the accepted value.
- Multiply that answer by 100 and add the symbol% to express the answer as a percentage.
Example calculation
Let us now try a sample problem.
You are given a cube of copper pure. You measure the sides of the cube to find the volume and weigh it to find its mass. When you calculate the density using your measurements, you get 8.78 grams / cm. 3. The accepted density of copper is 8.96 g / cm 3What is your error rate?
Solution:
experimental value = 8.78 g / cm 3
accepted value = 8.96 g / cm 3
Step 1: Subtract the accepted value from the experimental value.
8.78 g / cm 3 – 8.96 g / cm 3 = -0.18 g / cm 3
Step 2: take the absolute value of step 1
| -0.18 g / cm 3 = 0.18 g / cm 3
(0.18g/cm3)/(8.96g/cm3)=0,02
Step 3: Divide that answer by the accepted value.
Step 4: Multiply that answer by 100 and add the symbol% to express the answer as a percentage.
0,02 x 100 = 2
2%
The percentage error of your density calculation is 2%.