Percent error is the percent difference between a measured and expected value. (image: Sherman Geronimo-Tan)
Percent Error Definition
Percent error, sometimes referred to as percentage 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.
The formula for calculating percent error is:
Note: occasionally, it is useful to know if the error is positive or negative. If you need to know the positive or negative error, this is done by dropping the absolute value brackets in the formula. In most cases, absolute error is fine. For example, in experiments involving yields in chemical reactions, it is unlikely you will obtain more product than theoretically possible.
Steps to Calculate the Percent Error
- Subtract the accepted value from the experimental value.
- Take the absolute value of 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.
Now let’s try an example problem.
You are given a cube of pure copper. 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/cm3. Copper’s accepted density is 8.96 g/cm3. What is your percent error?
Solution:
experimental value = 8.78 g/cm3
accepted value = 8.96 g/cm3
Step 1: Subtract the accepted value from the experimental value.
8.78 g/cm3 – 8.96 g/cm3 = -0.18 g/cm3
Step 2: Take the absolute value of step 1
|-0.18 g/cm3| = 0.18 g/cm3
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 percent error of your density calculation was 2%.
Steps 1 and 3 use the wrong values. Since the experimental value is smaller than the accepted value it should be a negative error.
Thanks for pointing that out. The post has been corrected.
Mark is not correct. Percent error is always positive regardless of the values of the experimental and actual values. Please see my post to him.
Percent error is always represented as a positive value. The difference between the actual and experimental value is always the absolute value of the difference. |Experimental-Actual|/Actualx100 so it doesn’t matter how you subtract. The result of the difference is positive and therefore the percent error is positive.
Percent error is always positive, but step one still contains the error initially flagged by Mark. The answer in that step should be negative:
experimental-accepted=error
8.78 – 8.96 = -0.18
In the article, the answer was edited to be correct (negative), but the values on the left are still not in the right order and don’t yield a negative answer as presented.
What is the accepted value?
Say if you wanted to find acceleration caused by gravity, the accepted value would be the acceleration caused by gravity on earth (9.81…), and the experimental value would be what you calculated gravity as 🙂
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okay say you have two different percent errors, because of a word problem were there the end result id two groups of percent errors, how do you know which one is the accurate one.