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Percentage Calculator in Common Phrases
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
Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values.
P × V1 = V2
P is the percentage, V1 is the first value that the percentage will modify, and V2 is the result of the percentage operating on V1. 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
|= 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 =||
|= 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
How to Calculate Percentages
Calculating percentages can be an easy task. There are numerous percentage calculators online that can help with task by simply searching for “percentage calculator.” However, there may be a time when (however, unlikely it sounds) you may need to be able to calculate percentages without any digital assistance.
The word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred”. So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time.
The numbers that you will be converting into percentages can be given to you in 2 different formats, decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiple .87 by 100.
.87 × 100=87
Thus, resulting in 87 percent.
Percent is often abbreviated with the % symbol. Presenting your answer as 87% or 87 percent is acceptable.
given a fraction
If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.
13 ÷ 100 = .13
Then, follow the steps above for converting a decimal to a percent.
.13 × 100 = 13
Thus getting 13%.
The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.
Most of the time, you will be given a percentage of a given number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is. To calculate the percentage of a specific number, you first convert the percentage number to a decimal.
This process is the reverse of what you did earlier. You divide your percentage by 100. So, 40% would be 40 divided by 100 or .40.
40 ÷ 100 = .40
Once you have the decimal version of your percentage, simply multiply it by the given number. In this case, the amount of your paycheck. If your paycheck is $750, you would multiply 750 by .40.
750 × .40 = 300
Your answer would be 300. You are paying $300 in taxes.
Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1500, how much should you save?
Start by converting 25 percent to a decimal.
25 ÷ 100 = .25
Now, multiply the decimal by the amount of your paycheck, or 1500.
1500 × .25 = 375
You need to save $375 from each paycheck.
How To Calculate Percentage, Percentage Change and Percentage Difference
Knowing how to calculate the percentage of a number is a fundamental component of many aspects of life. For example, you may need to know how to calculate percentage to make a car payment or determine the down payment for a home.
Percentage calculations are also important in business and are used in 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 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.”
A percentage 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 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.
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 percentage problem would be “12.5 is 50% of 25.”
2. Finding the percentage
For a percentage 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 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 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 percentage problem, you would want to divide the whole by the percentage 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.
An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.