Percentage Difference Calculator
The percentage difference calculator is here to help you compare two numbers. Here we will show you how to calculate the percentage difference between two numbers and, hopefully, to properly explain what the percentage difference is as well as some common mistakes. In the following article, we will also show you the percentage difference formula. On top of that, we will explain the differences between various percentage calculators and how data can be presented in misleading but still technically true ways to prove various arguments.
If you want to compute the percentage difference between percentage points, check our percentage point calculator.
What is percentage difference?
To answer the question "what is percentage difference?" we first need to understand what is a percentage. A percentage is just another way to talk about a fraction. A percentage is also a way to describe the relationship between two numbers. For example, we can say that 5 is 20% of 25, or 2 is 5% of 40. When we talk about a percentage, we can think of the
% sign as meaning
1/100. Going back to our last example, if we want to know what is 5% of 40, we simply multiply all of the variables together in the following way:
5 × 1/100 × 40 = 200/100 = 2
If you follow this formula, you should obtain the result we had predicted before: 2 is 5% of 40, or in other words, 5% of 40 is 2. If you like, you can now try it to check if 5 is 20% of 25.
Now, if we want to talk about percentage difference, we will first need a difference, that is, we need two, non identical, numbers. Let's take, for example, 23 and 31; their difference is 8. Now we need to translate 8 into a percentage, and for that, we need a point of reference, and you may have already asked the question: Should I use 23 or 31? As we have not provided any context for these numbers, neither of them is a proper reference point, and so the most honest answer would be to use the average, or midpoint, of these two numbers.
We would like to remind you that, although we have given a precise answer to the question "what is percentage difference?", precision is not as common as we all hope it to be. It is very common to (intentionally or unintentionally) call percentage difference what is, in reality, a percentage change. This makes it even more difficult to learn what is percentage difference without a proper, pinpoint search.
We will tackle this problem, along with dishonest representations of data, in later sections. We hope this will help you distinguish good data from bad data so that you can tell what percentage difference is from what percentage difference is not. For now, though, let's see how to use this calculator and how to find percentage difference of two given numbers.
How to find the percentage difference?
To calculate the percentage difference between two numbers,
b, perform the following calculations:
- Find the absolute difference between two numbers:
|a - b|.
- Find the average of those two numbers:
(a + b) / 2.
- Divide the difference by the average:
|a - b| / ((a + b) / 2).
- Express the result as percentages by multiplying it by
- Or use Omni's percentage difference calculator instead 😃
And that's how to find the percentage difference! You can extract from these calculations the percentage difference formula, but if you're feeling lazy, just keep on reading because, in the next section, we will do it for you. Just remember that knowing how to calculate the percentage difference is not the same as understanding what is the percentage difference.
We have mentioned before how people sometimes confuse percentage difference with percentage change, which is a distinct (yet very interesting) value that you can calculate with another of our Omni Calculators. If you have read how to calculate percentage change, you'd know that we either have a 50% or -33.3333% change, depending on which value is the initial and which one is the final.
The percentage difference formula
Before we dive deeper into more complex topics regarding the percentage difference, we should probably talk about the specific formula we use to calculate this value. The percentage difference formula is as follows:
percentage difference = 100 × |a - b| / ((a + b) / 2)
To get even more specific, you may talk about a percentage increase or percentage decrease. To simply compare two numbers, use the percentage calculator. Or, if you want to calculate relative error, use the percent error calculator.
Now you know the percentage difference formula and how to use it. Please keep in mind that the percentage difference calculator won't work in reverse since there is an absolute value in the formula. This is why you cannot enter a number into the last two fields of this calculator.
When is the percentage difference useful and when is it confusing?
Now it is time to dive deeper into the utility of the percentage difference as a measurement. It should come as no surprise to you that the utility of percentage difference is at its best when comparing two numbers; but this is not always the case. We should, arguably, refrain from talking about percentage difference when we mean the same value across time. We think this should be the case because in everyday life, we tend to think in terms of percentage change, and not percentage difference.
For now, let's see a couple of examples where it is useful to talk about percentage difference. Let's say you want to compare the size of two companies in terms of their employees. In this example, company
C has 93 employees, and company
B has 117. To compare the difference in size between these two companies, the percentage difference is a good measure. In this case, using the percentage difference calculator, we can see that there is a difference of 22.86%. One key feature of the percentage difference is that it would still be the same if you switch the number of employees between companies. As we have established before, percentage difference is a comparison without direction.
It is, however, not correct to say that company
C is 22.86% smaller than company
B, or that
B is 22.86% larger than
C. In this case, we would be talking about percentage change, which is not the same as percentage difference. Another problem that you can run into when expressing comparison using the percentage difference, is that, if the numbers you are comparing are not similar, the percentage difference might seem misleading. Why?
Imagine that company
C merges with company
A, which has 20,000 employees. Now the new company,
CA, has 20,093 employees and the percentage difference between
B is 197.7%. Let's take it up a notch. Now a new company,
T, with 180,000 employees, merges with
CA to form a company called
CAT. We're not quite sure what this company does, but we think it's something feline-related.
CAT now has 200.093 employees. Now, the percentage difference between
CAT rises only to 199.8%, despite
CAT being 895.8% bigger than
CA in terms of percentage increase.
"How is this even possible?" That's a good question. The reason here is that despite the absolute difference gets bigger between these two numbers, the change in percentage difference decreases dramatically. The two numbers are so far apart that such a large increase is actually quite small in terms of their current difference. Therefore, if we want to compare numbers that are very different from one another, using the percentage difference becomes misleading. If you want to avoid any of these problems, we recommend only comparing numbers that are different by no more than one order of magnitude (two if you want to push it).
As with anything you do, you should be careful when you are using the percentage difference calculator, and not just use it blindly. In our example, the percentage difference was not a great tool for the comparison of the companies
B. At the end of the day, there might be more than one way to skin a
CAT, but not every way was made equally.
The meaning of percentage difference in real life
And we have now, finally, arrived at the problem with percentage difference and how it is used in real life, and, more specifically, in the media. The percentage difference is a non-directional statistic between any two numbers. However, when statistical data is presented in the media, it is very rarely presented accurately and precisely. Even with the right intentions, using the wrong comparison tools can be misleading and give the wrong impression about a given problem.
As for the percentage difference, the problem arises when it is confused with the percentage increase or percentage decrease. We have seen how misleading these measures can be when the wrong calculation is applied to an extreme case, like when comparing the number of employees between
B. But now, we hope, you know better and can see through these differences and understand what the real data means.
One other problem with data is that, when presented in certain ways, it can lead to the viewer reaching the wrong conclusions or giving the wrong impression. Let's take a look at one more example and see how changing the provided statistics can clearly influence on how we view a problem, even when the data is the same.
How to lie with data without lying?
The first thing that you have to acknowledge is that data alone (assuming it is rightfully collected) does not care about what you think or what is ethical or moral ; it is just an empirical observation of the world. What this implies, is that the power of data lies in its interpretation, how we make sense of it and how we can use it to our advantage.
Let's have a look at an example of how to present the same data in different ways to prove opposing arguments. Taking, for example,, we can change the impact of the data presented by simply changing the comparison tool we use, or by presenting the raw data instead. The unemployment rate in the USA sat at around 4% in 2018, while in 2010 was about 10%. Leaving aside the definitions of unemployment and assuming that those figures are correct, we're going to take a look at how these statistics can be presented.
For the first example, one can say that there has been an the unemployment rate has seen an overall decrease by 6% (
10% - 4% = 6%). Alternatively, we could say that there has been a percentage decrease of 60% since that's the percentage decrease between 10 and 4. Lastly, we could talk about the percentage difference around 85% that has occurred between the 2010 and 2018 unemployment rates.
If we, on the other hand, prefer to stay with raw numbers we can say that there are currently about 17 million more active workers in the USA compared to 2010. Or we could say that, since the labor force has been increasing over the last years, there are about 9 million less unemployed people, and it would be equally true. Just by looking at these figures presented to you, you have probably started to grasp the true extent of the problem with data and statistics, and how different they can look depending on how they are presented.
The important take away from all this is that we can not reduce data to just one number as it becomes meaningless. You should be aware of how that number was obtained, what it represents and why it might give the wrong impression of the situation. So just remember, people can make numbers say whatever they want, so be on the lookout and keep a critical mind when you confront information.
Is percentage difference equal to percentage change?
No, these are two different notions. In percentage difference, the point of reference is the average of the two numbers that are given to us, while in percentage change it is one of these numbers that is taken as the point of reference. Moreover, unlike percentage change, percentage difference is a comparison without direction.
What is the percentage difference between 20 and 30?
Let's go step-by-step and determine the percentage difference between 20 and 30:
- Compute the absolute difference between our numbers:
|20 - 30| = |-10| = 10;
- Compute also their average:
(20 + 30) / 2 = 50 / 2 = 25;
- Divide the difference by the average:
10 / 25 = 0.4; and
- Express the result as a percentage:
0.4 × 100 = 40%.
When is the percentage difference equal to 100%?
The percentage difference is equal to 100% if and only if one of the numbers is three times the other number. It's not hard to prove that! Look:
The percentage difference between
bis equal to 100% if and only if we have
|a - b| = (a + b) / 2.
With no loss of generality, we assume
a ≥ b, so we can omit the absolute value at the left-hand side. It follows that
2a - 2b = a + b
a = 3b, as claimed!