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# Percentage Change Calculator

By Kacper Pawlik and Mateusz Mucha

The percentage change calculator determines the percentage change between two values. It is particularly useful in many aspects of finance, chemistry and exponential growth and decay, as well as in other areas of mathematics. First, we need to know how to calculate percent change and to understand and use the percent change formula. To do this, we will provide you with many examples, each with in-depth analysis of various mathematical challenges and traps waiting for beginners.

Furthermore, we will teach you how to calculate percentage change when finding population growth rate, a fundamental statistic parameter describing processes happening in a particular population. We are sure that after reading the whole text the percentage change formula will stay in your head for a long time and you will be able to find the percent change in any situation.

## How to calculate the percent change?

Percentage change differs from percent increase and percent decrease in the sense that we can see both directions of the change. For example, the percent increase calculator calculates the amount of increase, in which we would say, "x percent increase". The percent decrease calculator calculates the amount of decrease, in which we would say, "x percent decrease". The percent change calculator would yield a result in which we would say, "x percent increase or decrease".

To calculate percent change we need to take the difference between the starting value and final value, divide by the absolute value of the starting value, and multiply the result by 100. The section below will go into more detail and show how to solve this problem.

## Percent change formula

The percent change formula is as follows:

`(new_value - original_value) / |original_value| * 100`

The two straight lines surrounding a number or expression (in this case `original value`) indicate the absolute value, or modulus. It means that if the value inside the straight lines is negative, we have to turn it into a positive one. The easiest way to do this is by erasing the minus before it. If the value inside the straight lines is positive, we don't need to do anything, it stays positive. After the absolute value is found, we can erase the straight lines or turn them into a bracket as they may serve this function as well.

You may ask how to calculate percent difference. It is the same thing as percent change, so you can use the percentage change calculator to accomplish this task as well. The general percentage formula for one quantity in terms of another is multiplying the ratio of the two quantities by 100. The percentage change calculator is not only useful in a classroom setting but also in everyday applications. The amount of sales tax on an item represents a percent change, as does the tip added to the bill at a restaurant. The ability to calculate the percentage change may come in handy, when negotiating a new salary or assessing whether the height of your child has increased appropriately. As you can see, knowing how to calculate percent change by hand using the percent change formula may be useful in the real-world.

## Percentage change formula – mathematical examples

Let's do a few examples together to get a good grasp on how to find percent change. In the first case, let's suppose that you have a change in value from `60` to `72` and you want to know the percent change.

1. Firstly, you need to input `60` as the original value and `72` as the new value into the formula.

2. Secondly, you have to subtract `60` from `72`. As a result, you get `12`.

3. Next, you should get the absolute value of `60`. As `60` is a positive number, you don't need to do anything. You can erase the straight lines surrounding `60`.

4. Now, you can divide `12` by `60`. After this division, you get `0.2`.

5. The last thing to do is to multiply the `0.2` by `100`. As a result, you get `20 %`. The whole calculations look like this:

`[(72 – 60) / |60|] * 100 = (12 / |60|) * 100 = (12 / 60) * 100 = 0.2 * 100 = 20 %`

6. You can check your result using the percentage change calculator. Is everything alright?

In the second example, let's deal with a slightly different example and calculate the percent change in value from `50` to `-22`.

1. Set `50` as the original value and `-22` as the new value.

2. Then, you need to perform a subtraction. The difference between `-22` and `50` is `-72`. Remember always to subtract the original value from the new value!

3. Next, you are obliged to get the absolute of `50`. As the original value in this example is also a positive number, then you can just erase the straight lines.

4. It is time to perform the division. `-72` divided by the `50` equals `-1.44`.

5. Finally, you have to multiply the result by `100`. Let's see. `-1.44` times `100` is `-144 %`. The whole process should look like this:

`[(-22 – 50) / |50|] *100 = (-72 / |50|) * 100 = (-72 / 50) * 100 = -1.44 * 100 = -144 %`

6. Remember that you can always check the result with the percent change calculator.

In the third and final example, we will work only with negative numbers. In this case, you will see that getting the absolute value, may change the final result of an equation. We will find a percent change between `-10` and `-25`.

1. First, let's assume that `-10` is the original value that is being changed into `-25`.

2. In the second step, as always, subtract the original value from the new one. `-25` reduced by `-10` is `-15`.

3. Let's concentrate during the third step, as it is different from what you have seen before. This time getting the absolute value will change something. Apply it to the original value `-10`. As it is negative, you have to erase the minus before it, thus, creating a positive value of `10`. You will see that this change will have a significant effect on the final result.

4. Now, let's divide `-15` by `10` that you got from the last step. `-15` divided by `10` is `-1.5`.

5. You can finish your calculation by multiplying `-1.5` by `100`. The final outcome is `-150%`. The full equation should look like this:

`[(-25 – (-10)) / |-10|] * 100 = (-15 / |-10|) * 100 = (-15 / 10) * 100 = -1.5 * 100 = -150 %`

6. As always, we encourage you to check this result with our percentage change calculator.

As you may have already observed, when the new value is smaller than the original one, the final result will be negative. Thus, you need to put a minus before it. On the other hand, if the new value is bigger than the original value, the result will be positive. You can use this to predict what the final result will be, and check your answer.

If you had used a negative instead of a positive for the absolute value in this example, then `-15` would have been divided by `-10`, giving you `1.5` as a result. It is a positive number, and your final answer would have been `150 %`. Your error would have been the difference between `-1.5` and `1.5`. This difference equals `3`, so our calculation would have ended with `300 %` of an error (`3 * 100% = 300 %`)! This is why you have to be careful when solving mathematical problems. A small mistake in one place may result in an enormous error in another.

We have a task for you! Calculate, using the methods we have described previously, what is the percentage change between `-20` and `-30`. Concentrate and watch out for mathematical traps that are waiting for you. But don't fear. By this point, you should know everything that is required to do it correctly. Remember to check your result using the percent change calculator.

## Population growth rate – example on how to find percent change

Population growth is the increase in the number of individuals of a certain population. It can be a population of people, but also cows, foxes or even flies. Members of any species can create a population. The population may be limited to a particular territory, country or expand to the whole world. You may count the number of dogs in your neighborhood, thus determining the population of dogs in the area surrounding your home. If you count their number after one year and compare it with the previous one, you will obtain their population growth. We can calculate it using this formula:

`current population – previous population = population growth`

When the population growth is higher than zero, it means that the population is increasing and the number of individuals is getting bigger with each year. However, when the population growth is negative (with a value below zero), then the population is becoming smaller and smaller. The population growth of 0 means that the population size is not changing at all.

You can then divide the population growth by the number of individuals in the previous population and times by 100 to get the population growth rate. It is a measure of population growth compared to the number of individuals forming the population in the previous period. Mathematically, it looks like this:

`(population growth / previous population) * 100 = population growth rate`

Combined, the whole formula can be written as:

`((current population – previous population) / previous population) * 100 = population growth rate`

Notice, that although it looks very similar to the formula for percentage change, you don’t need to get the absolute value of the previous population. It is because the population can never drop below zero, nor have a negative value. Population growth and population growth rate can however be negative, representing the decreasing number of individuals.

What is the difference between population growth and the population growth rate? Both of these parameters are ways of illustrating the change in the size of the population. Population growth is more direct and precise, as it shows us the exact difference between population size in two periods. However, the population growth rate also has its advantages. It emphasizes the dynamics of the process. It tells us how big the change is compared to the previous state of the population. Population growth of 20 may seem small, but if the original population was 10, then it means that the population size has doubled. The population growth rate shows it to us. In this case, its value would be 100 %.

Let's calculate one population growth rate together to make sure that this concept will stay with you for a while In 1990 in the United States there were 253,339,000 citizens. Over the next 20 years, the USA population was rising. In 2010 it reached 310,384,000 people.

1. First, let's calculate the population growth. You have to subtract the number of USA citizens in 1990 from the number of citizens in 2010:

`310,384,000 - 253,339,000 = 57,045,000`

2. Now, you can calculate the population growth rate. To do that, you need to divide the population growth by the number of citizens in the earlier period (in this case in 1990):

`57,045,000 / 253,339,000 = 0.225`

3. The last thing to do is multiply the acquired value by 100 to get the percent:

`0.225 * 100% = 22.5%`

4. After these calculations, you can say that the USA population increased by `22.5%` between the years 1990 and 2010. Congratulations!

You don't have to perform all the calculations by hand. Keep in mind that our percentage change calculator is always waiting for you at omnicalculator.com!

There is yet another situation in which you may want to use the percentage change calculator. If you have some spare money that you want to invest, you will have to choose between many investment offers. You may calculate the future growth of your savings with our investment calculator and compound annual growth rate calculator, and then get the percent change with the percentage change calculator. By comparing percent changes of different investment options, you will see which is the optimal one.

Kacper Pawlik and Mateusz Mucha

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