# How to calculate percentages - The theory

## Who invented percentages?

The final concept developed throughout history, so it was not a person who started using or introducing it. In Ancient Rome mathematical computation were expressed in fractions of 100. This later became the percentages we use now.

The word percent comes from the Latin phrase per centum, and it means "for each hundred." According to Cut the Knot, in 17th century Europe, the symbol o o was often used as an abbreviation for percent. This ancient symbol has evolved into the % symbol, which is commonly used today. For instance, 1 percent can be written as 1%, and it is the same as the fraction 1/100. Ten percent can be written as 10%, which is the same as the fraction 10/100. Likewise, a penny is 1 percent of a dollar, and a dime is 10 percent of a dollar.

For calculating percentage problems there are many formulas we can use. The most basic one would look like: X/Y = P x 100. The formulas listed below are all mathematical variations of this formula.

The three basic percentage problems would look like this. X and Y are number,  P is the percentage:

## Find P percent of X - Percentage Calculator 1

We will use the P% * X = Y formula here to find the percentage of a number. Let's calculate the 20% of 400:

• Let's convert the problem by using the percentage formula: P% * X = Y
• P is 20%, X is 400, so the equation is 20% * 400 = Y
• Convert 20% to a decimal by removing the percent sign and dividing by 100: 20/100 = 0.20
• Substitute 0.20 for 20% in the equation: 20% * 400= Y becomes 0.20 * 400 = Y
• Finally do the math: 0.20 * 400 = 80, Y = 80
• So 20% of 400 is 80

## Find what percent of X is Y - Percentage Calculator 2

Here we will use the percentage formula: Y/X = P% Let's see what percent of 40 is 6?

• Convert the problem to an equation using the formula: Y/X = P%
• X is 40, Y is 6, so the equation is 6/40 = P%
• Do the math: 6/40 = 0.15
• The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
• Converting 0.15 to a percent: 0.15 * 100 = 15%
• So 15% of 40 is 6.

## Find X if P percent of it is Y - Percentage Calculator 3

Let's use the percentage formula Y/P% = X to find out 10 is 20% of what?

• Convert the problem to an equation using the percentage formula: Y/P% = X
• Y is 10, P% is 20, so the equation is 10/20% = X
• Convert the percentage to a decimal by dividing by 100.
• Converting 20% to a decimal: 20/100 = 0.20
• Substitute 0.20 for 20% in the equation: 10/0.20 = X
• Do the math: 10/0.20 = X
• X = 50
• So 10 is 20% of 50