Find out what percent a number n is of another number M

One number can be expressed as a percentage of another number. For example, 3 out of 5 can be written as 60%. Expressing one number as a percentage of another is easy. Divide one number by the other number, then multiply by 100%.

What is 45 out of 60 as a percentage?

Divide 45 by 60.

45 ÷ 60 = 0.75

Multiply the answer (0.75) by 100%.

0.75 × 100% = 75%

What is 12 out of 60 as a percentage?

Start with the formula:

n1⁄n2 × 100%

Substitute the numbers into the formula. The formula is for n1 out of n2.In our example, we are finding 12 out of 60, so n1 = 12 and n2 = 60.

12⁄60 × 100% = 12 ÷ 60 × 100% 12⁄60 × 100% = 0.2 × 100% 12⁄60 × 100% = 20%

Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations.

How to Calculate Percentages

There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.

Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:

1. Find P percent of X
2. Find what percent of X is Y
3. Find X if P percent of it is Y

Read on to learn more about how to figure percentages.

1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y

Example: What is 10% of 150?

• Convert the problem to an equation using the percentage formula: P% * X = Y
• P is 10%, X is 150, so the equation is 10% * 150 = 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% * 150 = Y becomes 0.10 * 150 = Y
• Do the math: 0.10 * 150 = 15
• Y = 15
• So 10% of 150 is 15
• Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

2. How to find what percent of X is Y. 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
• Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
• Converting 0.20 to a percent: 0.20 * 100 = 20%
• So 20% of 60 is 12.
• Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%

3. How to find X if P percent of it is Y. 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

Remember: How to convert a percentage to a decimal

• Remove the percentage sign and divide by 100
• 15.6% = 15.6/100 = 0.156

Remember: How to convert a decimal to a percentage

• Multiply by 100 and add a percentage sign
• 0.876 = 0.876 * 100 = 87.6%

Percentage Problems

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.

• Written as an equation: Y = P% * X
• The 'what' is Y that we want to solve for
• Remember to first convert percentage to decimal, dividing by 100
• Solution: Solve for Y using the percentage formula
  Y = P% * X

• Written using the percentage formula: Y = 10% * 25
• First convert percentage to a decimal 10/100 = 0.1
• Y = 0.1 * 25 = 2.5
• So 10% of 25 is 2.5

• Written as an equation: Y = P% ? X
• The 'what' is P% that we want to solve for
• Divide both sides by X to get P% on one side of the equation
• Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
• Solution: Solve for P% using the percentage formula
  P% = Y ÷ X

• 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

• 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%

• 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

• 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

• Written using the formula: P% = 6 ÷ 27
• 6 ÷ 27 = 0.2222
• Convert decimal to percent
• P% = 0.2222 × 100
• P% = 22.22%
• So 22.22% of 27 is 6

• 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%

• 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.

• 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

• 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

• 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%

• 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%

• 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

• 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%

• 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

• Written using the formula: P% = Y / X
• 9 ÷ 13 = P%
• 9 ÷ 13 = 0.6923
• Convert decimal to percent by multiplying by 100
• 0.6923 * 100 = 69.23%
• 9 ÷ 13 = 69.23%
• So 9 of 13 is 69.23%

Related Calculators

Find the change in percentage as an increase or decrease using the Percentage Change Calculator.

Solve decimal to percentage conversions with our Decimal to Percent Calculator.

Convert from percentage to decimals with the Percent to Decimal Calculator.

If you need to convert between fractions and percents see our Fraction to Percent Calculator, or our Percent to Fraction Calculator.

References

Weisstein, Eric W. "Percent." From MathWorld -- A Wolfram Web Resource.