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One of the most useful formulas (or formulae) in chemistry, physics, and other sciences is the percentage error formula. If you would like to know how to calculate the percent error formula for chemistry, physics, etc., you have come to the right place.
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In this article, I will be talking about the percent error formula (also sometimes known a the percentage error formula. There will all the background and general information about this formula you will ever need including, of course, how you would go about calculating this formula accurately with some practical examples. So, by the end of it, I hope that you will be able to both understand the percent error formula and use it.
What Is The Percent Error Formula?
The first thing to say is that this formula is known by two different yet similar names: percent formula and percentage formula. Just for the sake of clarity and consistency, in this article, I will be referring to it as the percent formula. But know that they are one and the same thing so if you have come to this article looking to find out how to calculate how to calculate the percentage formula, you have indeed come to the right place!
Now I have cleared all of that out, here is what this formula achieves. The percent error is a percentage representation of the difference between the following two values: the approximate (or measured) value and an exact (known value). This formula is used as a way to determine how precise your calculations are.
“In my school, the brightest boys did math and physics, the less bright did physics and chemistry, and the least bright did biology. I wanted to do math and physics, but my father made me do chemistry because he thought there would be no jobs for mathematicians”. – Stephen Hawking.
The closest to zero the results of this formula is the closest you are getting to your targeted value. So this formula is used to establish how close to this are. It is the best way to find it if you are totally off the mark (as it were) or actually quite close to solving your experiment.
The formula is used in Physics, chemistry, and other sciences. So, there are two values at play here: the so-called experimental or measured value and the so-called exact or true value. The percent error formula is used to find out how close those two values are.
It is quite common for the percent error turns out to be positive value instead of a negative one in different applications. Having said that, it should also be noted that in some sciences such as chemistry normally the value is kept negative.
It is actually really important to know whether the error is positive or negative.
How Do You Calculate The Percent Error Formula For Chemistry, Physics, Etc.?
According to the “How To Calculate Percent Error” article in Thought Co. there are just a few simple steps involved in calculating this formula.
Here they are:
- The first thing that you will need to do is to subtract one value from another. The order in which you will need to do this will depend on whether you would like to keep negative signs or not. If you are going to drop the sign the order in which you subtract the values, then you can carry out the subtraction in any order you choose. If, however, you would like to keep the negative signs, then you will have to subtract the theoretical value from the experimental value. Once you have done this in whichever order fits what you’d like in terms of negative or positive signs, the value that results from this calculation is your actual “error”.
- Once you have calculated your actual “error”, you will need to divide that error either by the exact or ideal value. Your exact or ideal value is not your experimental or measured value. Once you have made this division, you should be left with a decimal number as a result.
- Then, what you will need to do is to take the decimal number that resulted from the previous calculation and convert it into a percentage by multiplying by 100.
- Finally, add the percent symbol (%) to that number. This is your percent error value.
If you are more of a visual version, the Math Is Fun website shows that this is what the formula actually looks like:
In this formula, the “|” symbols stand for absolute value. This means that any negative values become positive.
However, it should also be noticed that the formula could have certain variations. For example, instead of an exact value, a theoretical value could also be used instead. But, it is important to do this only when this theoretical value is well known.
Another alternative way of using this formula is by not using absolute values. If we do this, as we saw in the previous steps, the value that results from our calculations can either be positive or negative. This can actually be quite helpful in certain contexts.
If we choose that we do not want to use absolute values, the formula will need to be modified by removing the “|” symbols. It will, therefore, look like this:
Examples of Calculations Of The Percent Error Formula
Now that I have gone through all the different variations for this formula both in for of steps and as an actual visual formula, it is time to see this calculation in practice.
The first example has been taking for the Thought Co article I referenced earlier one.
What Is the Context of the Experiment: This is a lab experiment that involves a block of aluminum.
The objective of the Experiment: Your goal in this experiment is twofold: on the one hand you are been asked to calculate the dimensions of the block of aluminum; and, on the other hand, you will also need to calculate the displacement in a container with a volume of water that is also unknown.
In this example, you measure the density of the block of aluminum as 2.68 g/cm3
Then, as part of the experiment, you reckon that the density of the block of aluminum is 2.70 g/cm3 at room temperature.
With that information, you will now be in a position to calculate the percent error of your measurement.
So, here’s how you will do this.
Firstly, subtract one value from the other, like this: 2.68 – 2.70 = – 0.02
Then, you will have to decide whether you have to take the absolute value (i.e., remove the negative sign), or not. This will depend on your needs. In this case, we will remove the negative sign from – 0.02 and get, instead 0.02. This value (0.02) is the error.
Next, you will have to divide the error (0.02) by the true value, like this: 0.02 / 2.70 = 0.0074074.
What you will need to do next is to multiply this value by 100, like this: 0.0074074 x 100 = 0.74.
Finally, add the percentage sign (%) to the result in order to represent the percent error. So, in this case, 0.74 will become 0.74%.
So, according to this calculation, the percent error is just 0.74%. Remember that the closer you will get to zero, the better. There will also a percent error for any experiment and, as far as these go, a percent error of 0.74% is not bad at all.
You could also try this example without absolute values, which would result in a negative percent error.
To see this more clearly, let’s see an example from Math Is Fun that does not use absolute value. In this case, the characteristics of the experiment are as follows:
What Is the Context of the Experiment: The weather forecast was 20 mm of rain this morning. However, we got significantly more: 25 mm.
The objective of the Experiment: Your goal in this experiment is to calculate the percent error for this weather forecast.
Firstly, subtract one value from the other, like this: 20 – 25 = -5.
Next, you will have to divide the error (-5) by the true value, like this: -5 / 25 = 0.2.
What you will need to do next is to multiply this value by 100, like this: -0.2 x 100 = -20.
Finally, add the percentage sign (%) to the result in order to represent the percent error. So, in this case, -20 will become -20%.
So, according to this calculation, the percent error is just -20%. This is really quite a big percentage error, which means that the forecast estimate was way too low.
As you can see, calculating the percent error formula for chemistry, physics, etc. is actually quite simple if you just follow the formula carefully and know whether you need to operate with or without absolute values.
If you have any feedback on this article or would like to share your own tips or examples using the percent error formula, please leave us a message in the comments section below!