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# Percentage calculator

This calculator is a free online math tool that solves eight types of percentage problems. Just input the values into the sentence that best describes the problem involving percentages, and the calculator will generate a step-by-step solution.

Percentage Calculator
Online tool solves eight types of percentage problems.
help ↓↓ examples ↓↓
What is
percents of
?
Number
is what percent of
?
Initial value
increased to
Initial amount
raise by
%
Initial value
decreased to
Initial amount
reduce by
%
Initial amount
changed to
percents of
=

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EXAMPLES
example 1:ex 1:
Find 45% of 120.
example 2:ex 2:
What is 45% of 60 %
example 3:ex 3:
150 is what percent of 400?
example 4:ex 4:
What is the percentage increase from to 50 to 75?
example 5:ex 5:
The student received a 60% on a maths exam that included 20 problems. How many problems did the student properly answer on this test?
example 6:ex 6:
The whale population numbers 140 pairs. If the number of pairs increases by 8%, how many pairs will there be altogether?
example 7:ex 7:
The workforce at a corporation decreased from 40 to 29 personnel. What is the percentage decrease in the number of employees?
Find more worked-out examples in our database of solved problems..
TUTORIAL

## How to solve percentage problems?

This calculator solves eight different types of percenatge problems. We will use some examples to show each type.

### Type 1: What is x % of y?

Example:What is 40% of 60?

### Solution:

Step1: Change the word of to multiplication sign.

40% of 60 = 40% * 60

Step2: Change 40% to decimal number by dividing 40% by 100 [40% = 40/100 = 0.4]

40% * 60 = 0.4 * 60 = 24

### Type 2: x is what percent of y?

Example: 16 is what percent of 40?

### Solution:

Step1: Translate the words into an equation

 16 is what percent of 40 16 = x $\cdot$ 40

Step2: Solve for $x$

\begin{aligned} 15 &= x \cdot 40 \\ 40 \cdot x &= 15 \\ x &= \frac{15}{40} \\ x &= 0.375 \\ \end{aligned}

Step3: Multiply x by 100% to convert the result to a percentage.

$$0.375 = 0.375 \cdot 100 \% = 37.5 \%$$

### Type 3: Percentage increase

Example: Mark’s hourly salary is \$15. What is the percentage increase in the salary if it is raised to \$18?

### Solution:

To solve this problem, we apply the percentage increase formula:

$$\text{% increase} = \dfrac{ \text{final amount} - \text{ initial amount} }{ \text{ initial amount} } \times 100$$

After putting the initial amount to 15 and the final amount to 18, we get:

\begin{aligned} \text{% increase} &= \dfrac{ 18 - 15 }{ 15 } \times 100 = \\[1.2em] &= \dfrac{ 3 }{ 15 } \times 100 = \\[1.2em] &= 0.2 \times 100 = \\[1.2em] & = 20 \% \end{aligned}

### Type 4: Percentage decrease

Example: The workforce at a corporation decreased from 135 to 110 personnel. What is the percentage decrease in the number of employees?

### Solution:

To solve this problem we use percentage decrease formula:

$$\text{% decrease} = \dfrac{ \text{initial amount} - \text{ final amount} }{ \text{ initial amount} } \times 100$$

After putting the initial amount to 135 and final amount to 110 we get:

\begin{aligned} \text{% increase} &= \dfrac{ 135 - 110 }{ 135 } \times 100 = \\[1.2em] &= \dfrac{ 25 }{ 135 } \times 100 = \\[1.2em] &= 0.185 \times 100 = \\[1.2em] & = 18.5 \% \end{aligned}

### Type 5: What percent of X is Y?

Example: What percent of 80 is 25?

### Solution:

Step1: Translate the words into an equation

 What percent of 80 is 25 x $\cdot$ 80 = 25

Step2: Solve for $x$

\begin{aligned} x \cdot 80 &= 25 \\ x &= \frac{25}{80} \\ x &= 0.3125 \\ \end{aligned}

Step3: Express $x$ as a percentage by multiplying the result by 100%.

$$0.3125 = 0.3125 \cdot 100 \% = 31.25 \%$$
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