Percentage Calculator

Our percentage calculator is the perfect tool to calculate what percent of X is Y, find the total based on a value and percentage, or determine the value based on the total and percentage.

Being able to calculate and understand percentages is an important skill for many areas of academics and daily life. Knowing how to find the percentage of a whole, the percentage something has increased or decreased, and the percentage one amount is of another helps make sense of data, statistics, finances, and more.

What is a Percentage?

What exactly is a percentage? A percentage is simply a way to show a fraction out of 100. When we talk about 25 percent, or 25%, that means 25 out of 100 parts. Percentages allow us to easily express how much or how little of something there is.

Imagine you had 100 marbles, and 25 of them were red. You could say that 25 out of the 100 marbles (25/100) were red. Or you could say 25% of the marbles were red. Using percentages makes it easy to talk about parts of a whole without having to use fractions.

Finding the Percentage of Something

Okay, so how do you actually calculate and find the percentage of something? Let's break it down step-by-step:

First, identify the whole amount and the part you want to find the percentage for. Let's say the whole is 300 students, and the part is 180 students.

Next, divide the part by the whole to get the fraction:
180 students / 300 students = 0.6

Then, multiply that fraction by 100 to calculate the percentage:
0.6 x 100 = 60%

So 180 out of 300 students is 60% of the total students.

Some examples:
- If you get 18 out of 20 questions right on a test, you got 18/20 = 0.9, then 0.9 x 100 = 90% correct
- If a clothing store sold 75 out of 250 shirts, that's 75/250 = 0.3, then 0.3 x 100 = 30% of shirts sold

Finding the Percentage Between Two Numbers

Sometimes you need to calculate the percentage that one number is larger or smaller than another number. For example, if your sister is 5 feet tall and you are 5 feet 3 inches tall, you may want to know what percentage taller you are.

Here are the steps:
1) Subtract the smaller number from the larger number to get the difference
2) Divide that difference by the smaller number
3) Multiply by 100 to get the percentage

Let's use the example of you being 5 feet 3 inches (63 inches) and your sister being 5 feet (60 inches) tall:

63 inches - 60 inches = 3 inch difference
3 inch difference / 60 inches (smaller number) = 0.05
0.05 x 100 = 5%

So you are 5% taller than your sister.

Other examples:
- If a shirt originally cost $25 and went on sale for $20, the percentage cheaper is:
$25 - $20 = $5
$5 / $25 (original price) = 0.2
0.2 x 100 = 20% off
- If the population of a city grew from 95,000 to 101,000 people, the percentage increase is:
101,000 - 95,000 = 6,000
6,000 / 95,000 (original) = 0.0632
0.0632 x 100 = 6.32% increase

Finding the Percentage of a Number

You may also need to find what percentage one number is of another number. For example, if you scored 22 points in a basketball game, you may want to know what percentage of the team's 80 total points you scored.

The simple way is:
1) Divide the first number by the second number to get the decimal
2) Multiply that decimal by 100 to get the percentage

Using the example:
22 points / 80 total points = 0.275
0.275 x 100 = 27.5%

So you scored 27.5% of the total points

Other examples:
- If you drove 175 miles out of a 700 mile road trip, you went:
175 / 700 = 0.25
0.25 x 100 = 25% of the total distance
- If a shirt is on sale for $15 and the original price was $60, you are paying:
$15 / $60 = 0.25
0.25 x 100 = 25% of the original price

The Percentage Formula

There is also a handy percentage formula you can use for many percentage calculations:

Percentage = (Part / Whole) x 100

The "part" is the amount you want to find the percentage for, and the "whole" is the total amount.

For example, if there are 25 rainy days out of 90 total days, we can calculate:

Percentage of rainy days = (25 rainy days / 90 total days) x 100
= (0.277...) x 100
= 27.7%

Using this formula can make calculating percentages easier once you get the hang of it.

History of Percentages

The word "percent" comes from the Latin words "per centum" which literally mean "by the 100" or "for each 100." Percentages have their origins in the simpler concept of fractions, used for millennia by cultures around the world.

The specific percent sign we use today (%) developed in the 1600s, becoming popular after being used by a Dutch mathematician. Before that, people wrote out "per centum" or used fraction notation. The percent symbol made calculations much simpler and quicker.

Spelling - Percent or Per Cent?

Technically, both "percent" and the phrase "per cent" are considered correct. However, in modern English usage, most style guides recommend using the single word "percent" to avoid awkward phrasing.

You would say "75 percent" of something, not "75 per cent." But if you were discussing the general concept or term, you could say "We calculated the percentages" or "The per cent symbol was invented..."

So while both are technically correct spellings, "percent" is the more modern and preferable way to write it. Unless discussing it linguistically, always use the single word.

Percentage Points (or Percent Points)

The term "percentage point" refers to the units used to calculate the numerical difference between two percentages. If something increases from 40% to 44%, that is a difference of 4 percentage points (or 4 percent points).

Percentage points are not the same as percents. For example, if a team's winning percentage increases from 40% to 60%, they have gained 20 percentage points, but the actual percent increase is:

(60% - 40%) / 40% = 0.5 = 50% increase

So a 20 percentage point gain results in a 50% increase in the percentage. It's important not to confuse percentage points with percentages themselves when doing calculations.

FAQ

What is a percentage?

A percentage represents a fraction or ratio out of 100. It allows you to easily express how much or how little of something there is compared to the whole amount. For example, if you scored 85 points out of 100 on a test, you could say your score was 85%.

How do I calculate percentage?

To calculate what percentage x is of y:

1. Divide x by y to get the decimal value.
2. Multiply that decimal by 100 to convert it to a percentage.

For instance, if you ran 5 miles out of a 10-mile race, you would calculate:
5 miles / 10 miles = 0.5
0.5 x 100 = 50%
So you ran 50% of the total race distance.

How do I find what number x is if it's percent of y?

To find x when you know it is percent of y:

1. Convert p% to a decimal by dividing by 100 (e.g. 25% = 0.25)
2. Multiply that decimal by y

As an example, if a $50 shirt is on sale for 30% off, you can calculate the sale price:
30% = 0.3
0.3 x $50 = $15
So the shirt is $50 - $15 = $35 at 30% off.

How much is 75% of 240?

To calculate 75% of 240:

1. 75/100 = 0.75
2. 0.75 x 240 = 180

Therefore, 75% of 240 is 180.

Percentages are used for discounts, grades, statistics, and comparing values in many everyday situations. Having a firm grasp on the calculations makes working with percentages much simpler.

How do you calculate percentage growth?

To calculate the percentage growth (or increase) between two numbers:

1. Identify the original/starting number and the new/larger number after growth.
2. Subtract the original number from the new number to get the amount of increase.
3. Divide the amount of increase by the original number.
4. Multiply that result by 100 to get the percentage growth.

For example, if a town's population grew from 25,000 to 28,000 people:

1. Original population: 25,000
2. New population: 28,000
3. Amount of increase: 28,000 - 25,000 = 3,000
4. 3,000 / 25,000 = 0.12
5. 0.12 x 100 = 12%

So the town's population grew by 12% in that period.

How do you calculate a number from a percentage?

If you know a percentage but need to find the number it represents:

1. First identify the "whole" number the percentage is based on.
2. Convert the percentage to a decimal by dividing by 100.
3. Multiply that decimal by the whole number.

For instance, if a student scored 92% on a test with 50 total questions:

1. Whole number of questions = 50
2. 92% = 0.92
3. 0.92 x 50 = 46

So the student got 46 out of 50 questions correct with a 92% score.

How do you calculate annual percentage increase?

To calculate the annual percentage increase for something that grows over time:

1. Identify the starting value and the final value after one year.
2. Subtract the starting value from the final value to get the amount of increase.
3. Divide the amount of increase by the starting value.
4. Multiply by 100 to get the annual percentage increase.

For example, if your investment grew from $10,000 to $10,700 over one year:

1. Starting value: $10,000
2. Final value after 1 year: $10,700
3. Amount of increase: $10,700 - $10,000 = $700
4. $700 / $10,000 = 0.07
5. 0.07 x 100 = 7%

So your investment had an annual percentage increase of 7%.

How do you calculate percentage of marks/grades?

To calculate your percentage score on a test or assignment:

1. First, identify the total number of possible points or questions.
2. Next, identify how many points or questions you got correct.
3. Divide the number you got correct by the total possible number.
4. Multiply that result by 100 to get your percentage score.

For example, if a test had 80 points total and you earned 68 points:

1. Total possible points: 80
2. Points you earned: 68
3. 68 / 80 = 0.85
4. 0.85 x 100 = 85%

So you scored 85% on that test.

How do you calculate an increase by a percentage?

To calculate a new value after increasing an original value by a certain percentage:

1. Identify the original value and the percentage increase.
2. Convert the percentage to a decimal by dividing by 100.
3. Multiply the original value by the percentage decimal to get the amount of increase.
4. Add the amount of increase to the original value to get the new, increased value.

For example, to increase $500 by 20%:

1. Original value: $500
2. Percentage increase: 20% = 0.2
3. $500 x 0.2 = $100 increase
4. $500 + $100 = $600 new value

So increasing $500 by 20% results in a new value of $600.