In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol “%” or simply as “percent” or “pct.” For example, 35% is equivalent to the decimal 0.35, or the fraction.

### Percentage Formula

Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values.

P × V_{1} = V_{2}

P is the percentage, V_{1} is the first value that the percentage will modify, and V_{2} is the result of the percentage operating on V_{1}. The calculator provided automatically converts the input percentage into a decimal to compute the solution. However, if solving for the percentage, the value returned will be the actual percentage, not its decimal representation.

EX: P × 30 = 1.5

P = | 1.530 | = 0.05 × 100 = 5% |

If solving manually, the formula requires the percentage in decimal form, so the solution for P needs to be multiplied by 100 in order to convert it to a percent. This is essentially what the calculator above does, except that it accepts inputs in percent rather than decimal form.

### Percentage Difference Formula

The percentage difference between two values is calculated by dividing the absolute value of the difference between two numbers by the average of those two numbers. Multiplying the result by 100 will yield the solution in percent, rather than decimal form. Refer to the equation below for clarification.

Percentage Difference = | |V_{1} – V_{2}|(V_{1} + V_{2})/2 | × 100 |

EX: | |10 – 6|(10 + 6)/2 | = | 48 | = 0.5 = 50% |

### Percentage Change Formula

Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values, and dividing the result by the initial value, essentially calculating how much the initial value has changed.

The percentage increase calculator above computes an increase or decrease of a specific percentage of the input number. It basically involves converting a percent into its decimal equivalent, and either subtracting (decrease) or adding (increase) the decimal equivalent from and to 1, respectively. Multiplying the original number by this value will result in either an increase or decrease of the number by the given percent. Refer to the example below for clarification.

EX: 500 increased by 10% (0.1)

500 × (1 + 0.1) = 550

500 decreased by 10%

500 × (1 – 0.1) = 450

## What is percentage?

Percentage, which may also be referred to as percent, is a fraction of a number out of 100%. this means “per one hundred” and denotes a piece of a total amount.

*For example, 45% represents 45 out of 100, or 45 percent 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 you could say “it snowed 20% of the time.”*

this may be written in a few different ways. One way to write or denote a percentage 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. A percent can also be depicted by using a percent sign or “%.”*

## How to calculate percentage

There are a few different ways that a percentage can be calculated. The following formula is a common strategy used to calculate the percentage of something:

### 1. Determine the whole or total amount of what you want to find a percentage for

*For example, if you want to calculate the percentage of how many 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, which has 30 days.*

### 2. Divide the number that you wish to determine the percentage for

*Using the example above, let’s say that it rained 15 days out of the 30 days in April. You would divide 15 by 30, which equals 0.5.*

### 3. Multiply the value from step two 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.*

## Types of percentage problems

There are three main types of percentage problems you might encounter in both personal and professional settings. These include:

- Finding the ending number
- Finding the percentage
- Finding the starting number

### 1. Finding the ending number

The following is an example of a question that would require you to use a that 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 that

So, you would move to the second step as listed in the previous section. However, since you already have the percentage, instead of dividing you will want to multiply the percentage by the whole number. *For this equation, you would multiple 50%, or 0.5, by 25. This gives you an answer of 12.5. Thus, the answer to this this problem would be “12.5 is 50% of 25.”*

### 2. Finding the percentage

For a this problem in which you need to find the percentage, a question may be posed as the following: *“What percent of 5 is 2?”* In this example, you will need to determine in a this 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 this 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 the following: *“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 this problem, you would want to divide the whole by that given. *Using the example of “45% of what is 2?”, you would divide 2 by 45% or .45. This would give you 4.4, which means that 2 is 45% of 4.4.*

## 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 this change by dividing the whole value by the original value and then multiplying it by 100. The formula for solving a this change is the following:

- For a price or this increase:
**[(New Price – Old Price)/Old Price] x 100** - For a price or this decrease:
**[(Old Price – New Price)/Old Price] x 100**

An example of a price/percentage increase is as follows: *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 divide 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 is as follows: *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 be the following: *A product cost $25 last year and a similar product costs $30 this year. To determine the *This *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 from this year is 18% more than the cost of the product from last year.*