There are many formulas to calculate percentages and solve percentage problems. The most basic is X/Y = P x 100, and all others are variations of it by solving for the unknown variable.
Let's explore the three fundamental percentage problems. X and Y are numbers, and P is the percentage:
- Find Y where Y is P percent of X
- Find what percentage P of X is Y
- Find X if Y is P percent of it
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How to calculate the percentage of a number
Answer: Use the percentage formula: P% * X = Y
Example: What is 10% of 220?
- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 10%, X is 220, so the equation is 10% * 220 = Y
- Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substitute 0.10 for 10% in the equation: 10% * 220 = Y becomes 0.10 * 220 = Y
- Do the math: 0.10 * 220 = 22. So, Y = 22 and 10% of 220 is 22.
How to find what percent of X is Y
Answer: Use the percentage formula: Y/X = P%
Example: What percent of 60 is 12?
- Convert the problem to an equation using the percentage formula: Y/X = P%
- X is 60, Y is 12, so the equation is 12/60 = P%
- Do the math: 12/60 = 0.20.
- You now have the decimal form and must multiply it by 100 to get the percentage form.
- Converting 0.20 to percentage: 0.20 * 100 = 20%
- So 20% of 60 is 12.
How to find X if P percent of it is Y
Answer: Use the percentage formula Y/P% = X
Example: 25 is 20% of what number?
- Convert the problem to an equation using the percentage formula: Y/P% = X
- Y is 25, P% is 20, so the equation is 25/20% = 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: 25/0.20 = X
- Do the math: 25/0.20 = X
- X = 125
- So 25 is 20% of 125
- Double-check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125
How to convert a percentage to decimal form
- Remove the percentage sign and divide by 100
- 15.6% = 15.6/100 = 0.156
How to convert a decimal to percentage form
- Multiply by 100 and add a percentage sign
- 0.876 = 0.876 * 100 = 87.6%
Basic percentage problems and how to solve them
There are nine variations on the three basic problems involving percentages. See if you can match your problem to one of the samples below. The problem formats match the input fields in the calculator above. Formulas and examples are included.
What Y is P percent of X?
- Written as an equation: Y = P% * X
- The ‘what' is Y that we want to solve for
- Remember to first convert a percentage to decimal, dividing by 100
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: What is 10% of 25?
- Written using the percentage formula: Y = 10% * 25
- First, convert a percentage to a decimal 10/100 = 0.1
- Y = 0.1 * 25 = 2.5. So 10% of 25 is 2.5
Y is what percent P of X?
- Written as an equation: Y = P% * X
- We need to solve for P% so we
- Divide both sides by X to get P% on one side of the equation
- The equation becomes Y ÷ X = P% or P% = Y ÷ X
- Solution: Solve for P% using the percentage formula
P% = Y ÷ X
Example: 12 is what percent of 40?
- Written using the formula: P% = 12 ÷ 40
- P% = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- So 12 is 30% of 40
Y is P percent of what X?
- Written as an equation: Y = P% * X
- The ‘what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 9 is 60% of what?
- Writen using the formula: X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- X = 15
- So 9 is 60% of 15
What percent P of X is Y?
- Written as an equation: P% * X = Y
- The ‘what' is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- (P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X
- Solution: Solve for P% using the percentage formula
P% = Y ÷ X
Example: What percent of 30 is 4?
- Written using the formula: P% = 4 ÷ 30
- 4 ÷ 30 = 0.1333
- Convert decimal to percent
- P% = 0.1333 × 100
- P% = 13.3%
- So 13.3% of 30 is 4
P percent of what X is Y?
- Written as an equation: P% × X = Y
- The ‘what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 20% of what is 7?
- Written using the formula: X = 7 ÷ 20%
- Convert the percent to a decimal
- 20% ÷ 100 = 0.2
- X = 7 ÷ 0.2
- X = 35
- So 20% of 35 is 7.
P percent of X is what Y?
- Written as an equation: P% * X = Y
- The ‘what' is Y that we want to solve for
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: 5% of 29 is what?
- Written using the formula: 5% * 29 = Y
- Convert the percent to a decimal
- 5% ÷ 100 = 0.05
- Y = 0.05 * 29
- Y = 1.45
- So 5% of 29 is 1.45
Y of what is P percent?
- Written as an equation: Y / X = P%
- The ‘what' is X that we want to solve for
- Multiply both sides by X to get X out of the denominator
- (Y / X) * X = P% * X becomes Y = P% * X
- Divide both sides by P% so that X is on one side of the equation
- Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 4 of what is 12%?
- Written using the formula: X = 4 ÷ 12%
- Solve for X: X = Y ÷ P%
- Convert the percent to a decimal
- 12% ÷ 100 = 0.12
- X = 4 ÷ 0.12
- X = 33.3333
- 4 of 33.3333 is 12%
What Y of X is P percent?
- Written as an equation: Y / X = P%
- The ‘what' is Y that we want to solve for
- Multiply both sides by X to get Y on one side of the equation
- (Y ÷ X) * X = P% * X becomes Y = P% * X
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: What of 25 is 11%?
- Written using the formula: Y = 11% * 25
- Convert the percent to a decimal
- 11% ÷ 100 = 0.11
- Y = 0.11 * 25
- Y = 2.75
- So 2.75 of 25 is 11%
Y of X is what percent P?
- Written as an equation: Y / X = P%
- The ‘what' is P% that we want to solve for
- Solution: Solve for P% using the percentage formula
P% = Y / X
Example: 9 of 22 is what percent?
- Written using the formula: P% = Y / X
- 9 ÷ 13 = P%
- 9 ÷ 13 = 0.409
- Convert decimal to percent by multiplying by 100
- 0.409 * 100 = 40.9%. So 9 of 22 is 40.9%
Anastasios Antoniadis is the founder and editor-in-chief of BORDERPOLAR. He has been covering and writing about video games and technology for over 4 years. He is a 2014 graduate of the Department of Informatics and Telecommunications of the University of Athens. In his off-time, he enjoys playing video games, watching films and TV shows, reading, and enjoying the outdoors.
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