How To Calculate Percentage, Change and Difference
By Indeed Editorial Team
Updated May 19, 2022 | Published February 25, 2020
Updated May 19, 2022
Published February 25, 2020
Knowing how to calculate the percentage of a number is a fundamental action for many aspects of life. For example, you may need to know how to calculate percentage to estimate car payments or determine the down payment for a home.
Percentage calculations are also important in business and various professional settings such as when calculating taxes or employee raises. In this article, we explore what a percentage is, how to calculate different components of a percentage and the types of percentages.
What is percentage?
Percentage, which may also be referred to as percent, is a fraction of a number out of 100%. Percentage means "per 100" and denotes a piece of a total amount. For example, 45% represents 45 out of 100, or 45% of the total amount.
Percentage may also be referred to as "out of 100" or "for every 100." For example, you could say either "it snowed 20 days out of every 100 days" or "it snowed 20% of the time."
A percentage may be written in several ways. One way is to portray it as a decimal. For example, 24% could also be written as .24. You can find the decimal version of a percent by dividing the percentage by 100.
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How to calculate a percentage
The following formula is a common strategy to calculate a percentage:
1. Determine the total amount of what you want to find a percentage
For example, if you want to calculate the percentage of days it rained in a month, you would use the number of days in that month as the total amount. So, let's say we are evaluating the amount of rain during the month of April's 30 days.
2. Divide the number to determine the percentage
Using the example above, let's say that it rained 15 of the 30 days in April. You would divide 15 by 30, which equals 0.5.
3. Multiply the value by 100
Continuing with the above example, you would multiply 0.5 by 100. This equals 50, which would give you the answer of 50%. So, in April, it rained 50% of the time.
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Types of percentage problems
There are three main types of percentage problems you might encounter in both personal and professional settings. These include:
1. Finding the ending number
The following is an example of a question that would require you to use a percentage calculation to find the ending number in a problem: "What is 50% of 25?" For this problem, you already have both the percentage and the whole amount that you want to find a percentage of.
Since you already have the percentage, you will multiply the percentage by the whole number. For this equation, you would multiply 50%, or 0.5, by 25. This gives you an answer of 12.5. Thus, the answer to this percentage problem would be "12.5 is 50% of 25."
2. Finding the percentage
If you need to find the percentage, a question may be posed as "What percent of 5 is 2?" In this example, you will need to determine in a percentage how much of 2 is part of the whole of 5. For this type of problem, you can simply divide the number that you want to turn into a percentage by the whole. So, using this example, you would divide 2 by 5. This equation would give you 0.4. You would then multiply 0.4 by 100 to get 40, or 40%. Thus, 2 is equal to 40% of 5.
3. Finding the starting number
A percentage problem that asks you to find the starting number may look like "45% of what is 2?" This is typically a more difficult equation but can easily be solved using the previously mentioned formula. For this type of percentage problem, divide the whole by the percentage given. Using the example, you divide 2 by 45% or .45. This would give you 4.4, which means that 2 is 45% of 4.4.
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How to calculate percentage change
A percentage change is a mathematical value that denotes the degree of change over time. It is most frequently used in finance to determine the change in the price of a security over time. This formula can be applied to any number that is being measured over time.
A percentage change is equal to the change in a given value. You can solve a percentage change by dividing the whole value by the original value and then multiplying it by 100. The formula for solving a percentage change is the following:
For a price or percentage increase:
[(New Price - Old Price)/Old Price] x 100
For a price or percentage decrease:
[(Old Price - New Price)/Old Price] x 100
Here's an example of a price/percentage increase:
A TV cost $100 last year but now costs $125. To determine the price increase, you would subtract the old price from the new price: 125 - 100 = 25. You would then divide this by the old price: 25 divided by 100 equals 0.25. You will then multiply this number by 100: 0.25 x 100 = 25, or 25%. So, the TV price has increased by 25% over the past year.
An example of a price/percentage decrease:
A TV cost $100 last year but now costs only $75. To determine the price decrease, you would subtract the new price from the old price: 100 - 75 = 25. You will then divide this number by the old price: 25 divided by 100 equals 0.25. You would then multiply this by 100: 0.25 x 100 = 25. or 25%. This means the TV costs 25% less than it did in the previous year.
How to calculate percentage difference
You can use percentages to compare two different items that are related to each other. For example, you may want to determine how much a product cost last year versus how much a similar product costs this year. This calculation would give you the percent difference between the two product prices.
The following is the formula used to calculate a percentage difference:
|V1 - V2|/ [(V1 + V2)/2] × 100
In this formula, V1 is equal to the cost of one product, and V2 is equal to the cost of the other product.
An example of using this formula to determine the difference between product costs would include:
A product cost $25 last year and a similar product costs $30 this year. To determine the percentage difference, you would first subtract the costs from each other: 30 - 25 = 5. You would then determine the average of these two costs (25 + 30 / 2 = 27.5). You will then divide 5 by 27.5 = 0.18. You will then multiply 0.18 by 100 = 18. This means that the cost of the product this year is 18% more than the cost of the product from last year.
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