# Percentage Calculator

## Calculator Use

Solve percentage word problems. This calculator converts percentage word problems to an equivalent equation and solves for the unknown value.

Remember that P% = p ×100, and p = P% ÷ 100, where lower case p is the decimal form of P%.

For example, 15% = 0.15 × 100 and 0.15 = 15% ÷ 100.

### How to convert a percentage to a decimal:

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

### How to convert a decimal to a percentage:

- Multiply by 100 and append a percentage sign
- 0.156 becomes 0.156 * 100 = 15.6%

## Percentage Word Problems

There are nine basic word problems that involve percents. The following are the questions you might be asked. The word problem questions are converted to the equivalent equations you will need to solve to answer the questions. Each is followed by an example.

### What is ___% of ___?

- What is ___% of ___? or What is P% of X?
- Rewritten as an Equation: Y = P% × X
- The 'what' is Y that we want to solve for
- Solution: Solve for Y using Y = P% × X

**Example**:

- What is 10% of 25?
- First convert percent to a decimal 10%/100 = 0.1
- Y = 10% × 25 = 0.1 × 25 = 2.5
- Therefore, 2.5 is 10% of 25.

### ___ is what percent of ___?

- ___ is what Percent of ___? or Y is what Percent of X?
- Rewritten as an Equation: Y = P% × X
- The 'what' is P% that we want to solve for.
- Divide both sides by X and the X on the right cancels, then
- Y ÷ X = (P% × X) ÷ X becomes Y ÷ X = P% or P% = Y ÷ X
- Solution: Solve for P% using P% = Y ÷ X

**Example**:

- 12 is what percent of 40?
- Rewrite as 12 is P% of 40
- Solve for P%: P% = Y ÷ X
- Y ÷ X = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- Therefore, 12 is 30% of 40.

### ___ is ___% of what?

- ___ is ___% of what? or Y is P% of what?
- Rewritten as an Equation: Y = P% × X
- The 'what' is X that we want to solve for
- Divide both sides by P% and the P% on the right cancels, then
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X or X = Y ÷ P%
- Solution: Solve for X using X = Y ÷ P%

**Example**:

- 9 is 60% of what?
- Rewrite as 9 is 60% of X
- Solve for X: X = Y ÷ P%
- X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- X = 15
- Therefore, 9 is 60% of 15

### What percent of ___ is ___?

- What percent of ___ is ___? or What percent of X is Y?
- Rewritten as an Equation: P% × X = Y
- The 'what' is P% that we want to solve for.
- Divide both sides by X and the X on the left cancels, then
- (P% × X) ÷ X = Y ÷ X becomes P% = Y ÷ X
- Solution: Solve for P% using P% = Y ÷ X

**Example**:

- What percent of 27 is 6?
- Rewrite as P% of 27 is 6
- Solve for P%: P% = Y ÷ X
- 6 ÷ 27 = 0.2222
- Convert decimal to percent
- P% = 0.2222 × 100
- P% = 22.22%
- Therefore, 22.22% of 27 is 6.

### ___% of what is ___?

- ___% of what is ___? or P% of what is Y?
- Rewritten as an Equation: P% × X = Y
- The 'what' is X that we want to solve for
- Divide both sides by P% and the P% on the left cancels, then
- (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
- Solution: Solve for X using X = Y ÷ P%

**Example**:

- 20% of what is 7?
- Rewrite as 20% of X is 7
- Solve for X: X = Y ÷ P%
- First convert percent to a decimal
- 20% ÷ 100 = 0.2, then
- X = 7 ÷ 20% = 7 ÷ 0.2
- X = 35
- Therefore, 20% of 35 is 7.

### ___% of ___ is what?

- ___% of ___ is what? or P% of X is what?
- Rewritten as an Equation: P% × X = Y
- The 'what' is Y that we want to solve for
- Restructure the equation to get Y = P% × X
- Solution: Solve for Y using Y = P% × X

**Example**:

- 5% of 29 is what?
- Rewrite as 5% of 29 is Y?
- Solve for Y: Y = P% × X
- First convert percent to a decimal
- 5% ÷ 100 = 0.05
- Y = 5% × 29 = 0.05 × 29
- Y = 1.45
- Therefore, 5% of 29 is 1.45.

### ___ out of what is ___%?

- ___ out of what is ___%? or Y out of what is P%?
- Rewritten as an Equation: Y ÷ X = P%
- The 'what' is X that we want to solve for
- Multiply both sides by X and the X on the left cancels, then
- (Y ÷ X) × X = P% × X becomes Y = P% × X
- Divide both sides by P% and the P% on the right cancels, then
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X or X = Y ÷ P%
- Solution: Solve for X using X = Y ÷ P%

**Example**:

- 4 out of what is 12%?
- Rewrite as 4 out of X is 12%?
- Solve for X: X = Y ÷ P%
- First convert percent to a decimal
- 12% ÷ 100 = 0.12, then
- X = 4 ÷ 12% = 4 ÷ 0.12
- X = 33.3333
- Therefore, 4 out of 33.3333 is 12%.

### What out of ___ is ___%?

- What out of ___ is ___%? or What out of X is P%?
- Rewritten as an Equation: Y ÷ X = P%
- The 'what' is Y that we want to solve for
- Multiply both sides by X and the X on the left cancels, then
- (Y ÷ X) × X = P% × X becomes Y = P% × X
- Solution: Solve for Y using Y = P% × X

**Example**:

- What out of 25 is 11%?
- Rewrite as Y out of 25 is 11%?
- Solve for Y: Y = P% × X
- First convert percent to a decimal
- 11% ÷ 100 = 0.11, then
- Y = 11% × 25 = 0.11 × 25
- Y = 2.75
- Therefore, 2.75 out of 25 is 11%.

### ___ out of ___ is what percent?

- ___ out of ___ is what percent? or Y out of X is what percent?
- Rewritten as an Equation: Y ÷ X = P%
- The 'what' is P% that we want to solve for.
- Restructure the equation by moving P%: P% = Y ÷ X
- Solution: Solve for P% using P% = Y ÷ X

**Example**:

- 9 out of 13 is what percent?
- Rewrite as 9 out of 13 is P%?
- Solve for P%: P% = Y ÷ X
- 9 ÷ 13 = 0.6923
- Convert decimal to percent
- 0.6923 × 100 = 69.23%
- P% = 69.23%
- Therefore, 9 out of 13 is 69.23%.

## Additional Percentage Problems

Change in percentage as an increase or decrease can be calculated using Percentage Change Calculator while percentage conversions can be solved with Decimal to Percent, Percent to Decimal, Fraction to Percent, or Percent to Fraction.

### 1. How to calculate percentage of a number (P% * X = Y ):

How to solve for the percentage of a number:

- What is 10% of 150? in equation form is 10% * 150 = Y
- We need to first convert the percentage to an equivalent decimal to do our calculation.
- Converting a percentage to a decimal we remove the percentage sign and divide by 100
- Converting 10% to a decimal; 10% = (10/100) = 0.10
- 10% * 150 = Y becomes
- 0.10 * 150 = Y
- Y = 15
- Or, 10% of 150 is 15

Combining the calculations you can get the formula for **P% * X = (P/100) * X = Y** so 10% * 150 = (10/100) * 150 = 15

### 2. How to calculate percentage of one number to another, a ratio (Y/X = P%):

This calculation is converting a ratio or fraction to a percentage. For example, how to solve for the percentage of one number to another:

- 15 is what percent of 150? in equation form is 15/150 = P%
- 15/150 = 0.10
- We now need to convert the decimal to an percentage so we end up with a percentage
- Converting a decimal to a percentage we multiply by 100 and append a percentage sign to the result
- Converting 0.10 to a percent; 0.10 = (0.10 * 100) = 10%
- So, 15/150 = 10%
- Or, 15 is 10% of 150

Combining the calculations you can get the formula for ** Y/X = ((Y/X) * 100)% = P%** so 15/150 = ((15/150) * 100)% = 10%

### 3. How to calculate a value from the percentage part, a ratio (Y/P% = X):

How to solve for a value when you know what a percentage part is:

- 15 is 10% what number? in equation form is 15/10% = X
- We need to first convert the percentage to an equivalent decimal to do our calculation.
- Converting a percentage to a decimal we remove the percentage sign and divide by 100
- Converting 10% to a decimal; 10% = (10/100) = 0.10
- 15/10% = X becomes
- 15/0.10 = X
- X = 150
- Or, 15 is 10% of 150

Combining the calculations you can get the formula for **Y/P% = Y/(P/100) = X** so 15/10% = 15/(10/100) = 150

## References

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

**Cite this content, page or calculator as:**

Furey, Edward "Percentage Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.