Percentage calculations are used in almost all aspects of our everyday lives. Like discounts in shops, taxes added on bills, exam results, work progress, weather forecasts, and many more. Understanding and knowing how to calculate percentages is beneficial, so is this calculator. This calculator is designed to make every percentage calculation faster and making your everyday life so much easier.

## Definition

Figures in percent indicate proportions. Percentages refer to one part per hundred and are expressed using the % symbol. It is a fraction of one number over another multiplied by one hundred.

For instance; one over two or (½), looking into the fraction, we already know that ½ is half of something or half of a whole, but if we want to know what it is in percentage, then we multiply it by 100. Thus, ½ × 100 = 0.5 × 100 = 50 % implies that one divided by two (½) equals fifty percent.

Percentages can also be expressed as a fraction of 100, decimals, or ratios; for instance, 50 % means the same as 50/100, 0.50, or 50:100.

There are several ways to calculate percentages. In the following sections, we are going to cover different calculations based on our calculator with useful and detailed explanations.

## Percentage Value

The percentage value is used to express the proportion portion of the total. For example, if 50 % of 100 is 50, then 50 is the percentage value. It is determined by multiplying the percentage rate by the original value and dividing by 100.

Let us refer to the question from the calculator. **What is 15 % of 520?**

We are asked to find 15 % out of 520. To determine the percentage value, we multiply the percentage rate by the original value and divide the result by 100.

Let **V _{1} = 15** and

**V**, and plug the values into the percentage value formula.

_{2}= 52015 % is multiplied by 520 and divided by 100.

Therefore, 15 % of 520 is 78.

**Let’s try another example:** A pair of shoes is worth $40 and is on sale with a 20 % discount. How much is the discount?

In this case, we are asked to determine how much 20 % of $40 is.

Let **V _{1} = 20** and

**V**, and plug the values into our formula.

_{2}= 4020 % of 40 is 8, which means the pair of shoes has $8 off the original price.

## Percentage Rate

The percentage rate is the percentage without the % symbol. The process of calculating the percentage rate is the reverse to that of calculating the percentage value. It is determined by dividing the percentage value by the original value and multiplying by 100.

Let us refer to the question from the calculator. **78 is what percent of 520?**

We are asked to find the percentage rate of 78 out of 520. To determine the percentage rate, we divide the percentage value by the original value and multiply by 100.

Let **V _{1} = 78** and

**V**, and set the values into the percentage rate formula.

_{2}= 52078 divided by 520 and multiplied by 100 = (78 / 520) × 100 = 0.15 × 100 = 15 %.

Therefore, 78 is 15 % of 520.

**Another example:** There are 27 females out of 60 students in Mr. Smith’s Math class. What percent are females from the class?

Let **V _{1} = 27** and

**V**, and set the values into our formula.

_{2}= 60Therefore, 45 % of the students in Mr. Smith’s math class are females.

## Reverse Percentage

Reverse percentages are used when we want to find the original value, and the percentage value and the percentage rate are given. We determine the original value by multiplying the percentage value by 100 and then dividing by the percentage rate.

Let us take the question from the calculator. **78 is 15 % of what number?**

To determine the original value, we multiply the percentage value by 100 and divide the result by the percentage rate.

Let **V _{1} = 78** and

**V**, then fill the values into the reverse percentage formula.

_{2}= 1578 multiplied by 100 divided by 15 = (78 x 100) / 15 = 520

Therefore, 520 is the original value.

**Try a different example:** Mrs. Brown has a 25 % frequent flyer discount for an airline, and she saved $183 for her plane ticket. How much was the original price of the ticket before the discount?

Let **V _{1} = 183** and

**V**, and fill the values into our formula.

_{2}= 25Therefore, the original price of Mrs. Brown’s plane ticket is $732.

## Percentage Change

The percentage change, be it a positive or a negative, is the change between an old and a new value. It is determined by subtracting the old value from the new value, then dividing the answer by the absolute old value and multiplying it by 100. A positive change expresses an increase, while a negative change expresses a decrease.

First, we take the question from the calculator: **What is the percentage change from 24 to 30?**

We are asked to find the change from 24 to 30 in percent. If we look into the given values, we can already determine an increase since the new value is higher than the old one.

Let **V _{1} = 24** and

**V**and fill in the values to the percentage change formula.

_{2}= 30Therefore, we have an increase of 25 % from 24 to 30.

**Another example:** At a computer store, the price of a laptop has dropped from $750 to $600. What is the percentage change?

**V _{1} = 750** and

**V**

_{2}= 600The price of the laptop decreased by 20 %.

**Note:** the symbol "|" indicates an absolute value, which means any negative values become positive.

## Percentage Difference

The percentage difference is a difference in percent between two positive numbers. The percentage difference between the given numbers is the absolute value of the difference between these numbers, divided by the average and multiplied by 100.

The example from the calculator says: **What is the percentage difference between 80 and 120?**

The order of the values doesn’t matter, as we are merely dividing the difference between two values by the average to get its percentage difference.

Let **V _{1} = 80** and

**V**and fill the values into the percentage difference formula.

_{2}= 120Therefore, the percentage difference between 80 and 120 is 40 %.

Keep in mind that the percentage difference is an absolute value; in this case, the negative result becomes positive.

**Another example:** Sam and John decided to buy themselves a new phone. Sam’s phone costs him $750, while John’s is $850. How much is the difference between the costs of the two phones?

Remember that the order of the values doesn’t matter so that we can put in **V _{1} = 750** and

**V**into our formula.

_{2}= 850Therefore, there is a 12.5 % difference in the costs between the two phones.