# How To Calculate Percentages (With Formula and Examples)

Updated July 31, 2023

Calculating percentages is an easy mathematical process to carry out, and it's a useful skill for both personal and work life. Sometimes, when there's the need to find the ratio or the portion of a quantity as a part of another quantity, you'll need to express it as a percentage.

In this article, we'll discuss percentage and how to calculate it, plus we'll review three types of percentage problems and examples of how to calculate percentage difference, a percentage increase and percentage decrease.

## What is percentage?

 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Definition: Percentage, often referred to as percent, is a fraction of 100.

Mathematically, "percentage" refers either to numbers or ratios that are expressed as fractions of 100. They're usually denoted as "%" or "percent." An example of a percentage is 65% or 65 percent. They might be further represented as simple fractions or decimal fractions (i.e., 65/100, 0.65).

The term "percentage" is formed from two small words: “per” and “cent.” Cent is a word with Latin and French origins and translates to "hundred," therefore "percent" literally means "per hundred." Calculating percentage means finding the share of a whole in terms of 100. It can be calculated manually or by using online calculators like the one below:

Semester 1

Related: Applied Math vs. Pure Math: What Are the Differences?

## How to calculate a percentage

Here are three steps to calculating a percentage based on the formula:

 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Percentage = (Value / Total value) × 100

### 1. Determine the format of the initial number

The number to be converted to a percentage can either be in decimal or fraction form. For example, a decimal number is 0.57 a fraction is 3/20. The number's initial format will determine the next mathematical process carried out on the number.

• 0.57

• 3/20

### 2. Turn the number into a decimal (if needed)

If the number to be converted to a percentage is a decimal like 0.57, you may not need to do anything before you go on to the next step. However, if it's a fraction, like 3/20, first divide the numerator (the top number 3) by the denominator (the bottom number 20) to get the decimal. For example, for 3/20:

• 3/20 = 0.15

### 3. Multiply the decimal number by 100

If you're required to convert a decimal number like 0.57 into a percentage, multiply it by 100. For example:

• 0.57 x 100 = 57%

• 0.03 x 100 = 3%

For a fraction, calculate the decimal first, then multiply the decimal by 100:

• 3/20 = 0.15 x 100 = 15%

Related: How To Calculate the Percentage of a Number

## Types of percentage problems

There are three common types of percentage problems you could see in personal or work settings. These include finding the ending number, finding the percentage and finding the starting number. All three can be solved by calculating for the missing part of the percentage formula: Percentage = (Value / Total value) × 100

 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Finding the ending number Finding the percentage Finding the starting number Question: "What is 50% of 25?" "What percent of 5 is 2?" "45% of what is 2?" Solution: Multiply the percentage by the total value Divide the value 2 by the total 5 and multiply by 100 Divide the ending number 2 by the percentage 45% Equation: .50 x 25 = 12.5 (2/5) x 100 = 40% 2/.45 = 4.4

Related: What Does a Finance Manager Do?

## Percentage calculation examples

Here are a few examples of finding the percentage in certain situations:

### 1. Calculating the original price

The price of a laptop was reduced by 30% to \$120. What was the original price?

• Find the percentage of the original or real number. In this case, it's \$120.

• Multiply the final number by 100. \$120 x 100 = \$12,000

• Divide the result of the multiplication by the percentage. \$12,000 divided by 30% = \$400.

• Thus, \$120 is 30% of \$400. Therefore, the original number was \$400.

You can double-check your answer by dividing \$400 by 100. 100 represents 10% of the total. \$40 x 3 = \$120.

Related: How To Calculate Percentage Decrease (With Examples)

### 2. Calculating the sale price

Find the sale price if a 20% discount is allowed off the marked price of \$30.

• Convert the percentage to a decimal. 20 divided by 100 = .20

• Multiply the decimal by the original price to get the discount amount. 20 X \$30 = \$6

• The \$30 price is discounted by \$6 for a total of \$24.

### 3. Calculating the new price

Two years ago, a football ticket was \$20. This year, it has increased by 60%. What is the price of this year's ticket?

• Divide the percentage increase by 100 to determine its decimal form. 60% divided by 100 = 0.6

• Then, multiply the decimal by the original price. 0.6 x \$20 = \$12

• Add the price of the original ticket and the amount of increase to find the new ticket price. \$20 + \$12 = \$32

• \$32 is the cost of the new ticket.

Related: What Is the Percentage Increase Formula? With Examples

## Percentage difference

You can also use percentages to compare two related items. For example, you may want to determine how much a product cost last year versus how much a similar product costs for the current year. This calculation would give you the percent difference between the two products' prices. The formula used to calculate a percentage difference is:

 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Percentage difference = |V1 - V2| / [(V1 + V2) /2] × 100

Where:

• V1 is equal to the cost of one product.

• V2 is equal to the cost of the other product.

Example of percentage difference:
A kitchen skillet cost \$25 last year and a competitor’s skillet costs \$30 this year. To determine the percentage difference, first subtract the costs from each other: 30 - 25 = 5. You then determine the average of these two costs (25 + 30 divided by 2 = 27.5). Divide 5 by 27.5 = 0.18 and then multiply 0.18 by 100 = 18. This means the cost of the competitor’s skillet this year is 18% more than the cost of your skillet last year.

30 - 25 = 5
25 + 30 = 55 / 2 = 27.5
5 / 27.5 = 0.18
0.18 x 100 = 18%

Read more: How To Calculate Percentage Difference

## Percentage change

A percentage change is a mathematical value that shows the degree of change over time. It is frequently used in finance to determine the change in the price of a security over time. The formula for solving a percentage change is the following:

 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Percentage increase = [(New Price - Old Price) / Old Price] x 100
 .css-1g5t2dl{font-family:"Noto Sans","Helvetica Neue","Helvetica","Arial","Liberation Sans","Roboto","Noto",sans-serif;font-weight:inherit;color:#595959;font-size:1.25rem;line-height:1.5;color:#2d2d2d;margin-bottom:0;font-size:1rem;margin-top:1.5rem;}html[lang=ja] .css-1g5t2dl{font-size:1rem;line-height:1.75;}@media screen and (min-width: 62em){.css-1g5t2dl{font-size:1.25rem;margin-top:2.5rem;}}Percentage decrease = [(Old Price - New Price) / Old Price] x 100

Example of a percentage increase:
A TV cost \$100 last year but now costs \$125. To determine the price increase, you subtract the old price from the new price: 125 - 100 = 25. Next,  divide this by the old price: 25 divided by 100 = 0.25. You then multiply that number by 100: 0.25 x 100 = 25, or 25%. So, the TV price has increased 25% over the past year.

125 - 100 = 25
25 / 100 = .025
.025 x 100 = 25%

Related: How To Calculate Trend Percentage (With Examples)

Example of a percentage decrease:
A TV cost \$100 last year but now costs only \$75. To determine the price decrease, you subtract the new price from the old price: 100 - 75 = 25. Divide his number by the old price: 25 divided by 100 = 0.25. You then multiply that number by 100: 0.25 x 100 = 25. or 25%. This means the TV costs 25% less than it did the year before.

100 - 75 = 25
25 / 100 = 0.25
.25 x 100 = 25%

Read more: How To Calculate Percentage Decrease

How is calculating percentages useful in financial analysis and budgeting?

Calculating percentages in financial analysis and budgeting helps track and analyze expenses, income and financial ratios. Using them, you can compare different categories, identify cost-saving opportunities and evaluate the financial health and performance of an organization.

What are some applications of percentages in sales and marketing?

In sales and marketing, you may use percentages to measure sales growth, market share, conversion rates and return on investment. They can assess overall sales performance, identify trends and evaluate the success of marketing campaigns, providing insights for future decision-making and strategy development.

How are percentages helpful in analyzing statistical data and research findings?

By using percentages in your statistical data analysis and research, you may be able to present and interpret specific figures more effectively. You can use percentages to summarize survey results, express probabilities and frequencies, normalize data for comparisons and calculate correlation coefficients to explain the relationships between variables. This facilitates understanding, guides you to conclusions and supports evidence-based decision-making.

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