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 to properly understand what is the percentage difference and what is not. In the following sections, 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 true, ways to prove various arguments.

What is percentage difference?

To answer the question of what is percentage difference, we first need to understand what is the percentage. A percentage is just another way to talk about a fraction. The percentage is also a way to talk about 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 together in the following way:

5 * 1/100 * 40 = 200/100 = 2,

and obtain the result we had predicted before: 2 is 5% of 40, or in other words, 5% of 40 is 2.

If we now want to talk about percentage difference we will need a difference first, that is, we need two 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 the doubt might come to your mind: Should I use 23 or 31? Under normal circumstances, none of them is a proper reference point, and the most honest answer would be to use the average, or midpoint between those two numbers.

We would like to remind you that we have talked about the precise definition of what is percentage difference, but precision is not as common as we all hope it would. It is very common to (intentionally or unintentionally) call percentage difference what in reality is a percentage change. It makes it more difficult to learn what is percentage difference without a proper search.

We will tackle these problems, along with dishonest representations of data in later sections, and we will help you distinguish good data from bad data so that you can tell what is percentage difference from what 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?

Let's use 20 and 30 as an example to see how to calculate percentage difference. We will need to divide the absolute difference by the average of those two numbers and express it as percentages. The calculation scheme is as follows:

  • find the absolute difference between two numbers: |20 - 30| = |-10| = 10
  • find the average of those two numbers: (20 + 30) / 2 = 50 / 2 = 25
  • divide those two: 10 / 25 = 0.4
  • express it as percentages: 0.4 * 100 = 40%
  • ... or use the percentage difference calculator :-)

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 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 our other Omni Calculator. If you read how to calculate percentage change, you'd know that we have either 50% or -33.3333% change, depending on which value is initial and which one is 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.

Now you know the percentage difference formula and how to calculate it. Please keep in mind that since there is an absolute value in the formula, the percentage difference calculator won't work in reverse. Hence the calculator you can't enter number in two last calculator's fields.

When is the percentage different useful and when it's not?

Now it is time to dive deeper into the utility of the percentage difference as a measurement. It would come as no surprise to you that the utility of percentage difference is at its best when comparing two numbers; but not always. We should, arguably, refrain from talking about percentage difference when we mean the same value across time. We think so 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, the company K will have 93 employees, and company B 117. To compare the difference in size between these 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 K is 22.86% smaller than B or that B is 22.86% bigger than K. 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 K merges with company O who has 20.000 employees. Now the new company, let's call it KO, has 20.093 employees and the percentage difference between KO and B is 197.7%. Let's take it up a notch. Now a new company, T, with 180.000 employees merges with KO to form (crowd's favorite) company called KOT, this new company would have now 200.093 employees. Now, the percentage difference between B and KOT rises only to 199.7% despite KOT being 895.8% bigger than KO in terms of percentage increase.

"How is this even possible?" - you might be rightfully asking. The reason here is that as the absolute difference gets bigger between two numbers, their percentage difference change decreases. Therefore, if we want to compare numbers that are very different from one another, using the percentage difference becomes misleading. Our recommendation to avoid any of these problems is to only compare numbers that are no more than one (two if you want to push it) orders of magnitude. If you want to learn more about orders of magnitude and what they mean, we recommend our scientific notation calculator.

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 to compare KOT and B companies. At the end of the day, there might be more than one way to skin a cat but not every way is equally good.

The meaning of percentage difference in real life

And now we arrive at the problem with percentage difference and how it is used in real life, more specifically in the media. The percentage difference is a non-directional statistics 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 different these measures can be when applied to extreme cases, like when comparing the number of employees between KOT vs B. But now you know better and can see through these differences, and understand what the real data means.

One other problem with data is that the way it is presented, can lead to the wrong conclusions or give the wrong impressions. 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) do not care about what you think or what is ethical or moral ; it just is. What this implies, is that the power of data lies in its interpretation, how we make sense of it and how we can apply it to our advantage.

Let's see an example of how to present the same data in different ways that seem to prove opposing arguments. Taking, for example, unemployment rates in the USA, we can change the impact of the data presented, by simply changing the comparison tool we use or presenting raw data instead. The unemployment rate in the USA sat 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.

In a first attempt, one can say that there has been an overall decrease in the unemployment rate of 6% (which is 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% between unemployment rates in 2010 and 2018.

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 as well say, since the work labor has been decreasing over the last years, there are about 9 million less unemployed people, and it would be equally true. Probably just by looking at these figures presented to you, you have started to grasp what the problem is 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 lie, so be on the lookout and keep a critical mind when you confront information.

Mateusz Mucha and Álvaro Díez - PhD candidate.

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