Percentage Change Calculator

The percentage change calculator determines the percentage change between two values. It is particularly useful in finance, chemistry, physics, and mathematics. Continue reading if you want to:

• Learn how to calculate percentage change;
• Understand and use the percent change formula;
• See examples of percent change computations, each with an in-depth analysis of mathematical challenges and traps waiting for beginners; and
• Learn about population growth rate, a real-life application of our percent change formula.

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!

Percent change differs from percent increase and percent decrease because we can see both directions of the change. For example, the percent increase calculator calculates the rate of increase between two values. Regardless of which value is larger, the calculator always gives an answer of the form "x percent increase". If the final value is less than the initial value, then we have a decrease, and x is simply a negative number (since we can think of a decrease as a "negative increase"). Similarly, the percent decrease calculator calculates the rate of decrease and outputs "x percent decrease" regardless of which value is larger.

By contrast, the percent change calculator yields an answer "x percent increase" if the final value is larger than the initial value; otherwise, it outputs "x percent decrease".

Let's explain in more detail how to calculate percent change.

To calculate percent change, we need to:

1. Take the difference between the initial value and the final value.
2. Divide by the absolute value of the initial value.
3. Multiply the result by 100.
4. Or use Omni's percent change calculator! 🙂

As you can see, it's not hard to calculate percent change. If you're interested in the mathematical formula for percentage change, we invite you to read the next section.

The percent change formula is as follows:

The vertical lines surrounding a number (in this case, $\rm initial$) indicate it is the absolute value, or modulus. Mathematicians define the absolute value |x| of a number x as its distance from 0, but really, you should think of it as "the value of x without the minus sign". If x is positive or 0, then its absolute value is the same as x (e.g. |3.5| = 3.5), and if 'x' is negative, then we simply erase the minus sign (e.g. |-3.5| = 3.5).

If you want to know how to calculate the percent difference, you should check the percentage difference calculator. But if you are only looking for the difference between the initial and final values, this percent change calculator will help you.

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 the classroom 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. Calculating the percentage change may come in handy when negotiating a new salary or assessing whether your child's height 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.

Let's do a few examples together to get a good grasp on how to find a 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, its absolute value is simply 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 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%

   The result is positive, and so 72 is a 20% increase of 60.

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 vertical lines.

4. It is time to perform the division. -72 divided by 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%

   The result is negative, and so -22 is a 144% decrease of 50.

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

As you may have already observed, the final result will be negative when the new value is smaller than the original one. 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 the outcome and check your answer.

Let's calculate together the percent change from -10 to -25:

1. Subtract the original value from the new one. -25 reduced by -10 is -15.

2. Compute the absolute value of the original value. As -10 is negative, you have to erase the minus before it, thus creating a positive value of 10.

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

4. 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%

5. As always, we encourage you to check this result with Omni's percentage change calculator.

If you forgot to replace -10 with its absolute value 10 in the denominator, then -15 would be divided by -10, giving you 1.5 as a result. This is a positive number, so your final answer would be 150% rather than -150%. This would mean that -25 is a 150% increase of -10: an obvious mistake since -25 is much smaller than -10. You must be careful while solving mathematical problems because a small mistake in one place may result in an enormous error in another.

We have a task for you! Using the methods above, calculate the percentage change between -20 and -30. Concentrate and watch out for mathematical traps 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 is the increase in the number of individuals in 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 or country or expand to the whole world. You can 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, the population is increasing, and the number of individuals is getting bigger each year. However, when the population growth is negative (with a value below zero), the population becomes smaller. A population growth of 0 means that the population size is not changing at all.

Let us see how to find the rate of change or the growth rate of the population. First divide the population growth by the number of individuals in the previous population, and then multiply it 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, we can write the whole formula 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. 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 measures illustrate the change in the population size. Population growth captures the absolute difference between population sizes in two periods, telling us by how many individuals the population has increased or decreased. In contrast, the population growth rate tells us the rate at which the population has grown or declined compared to its previous state. It emphasizes the dynamics of the process. A population growth of 20 may seem small, but if the original population consisted of 10 individuals, then it means a trifold increase in size, or equivalently, an increase by 200%.

Let's go together through an example to see how to find the population growth rate. Between 1990 and 2010, the number of United States citizens rose from 253,339,000 to 310,384,000.

1. Let's calculate the population growth. You have to subtract the number of US 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, it's 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 US population increased by 22.5% between 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 Omni Calculator!

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. By comparing interest rates (i.e., percent changes) of different investment options, you will find the optimal one.