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Percentage calculator
Percentage calculator is a free online tool that solves eight different types of percent-related problems. To get a step-by-step solution for percentage problemssimply enter the values in the appropriate sentence.
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 · 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 problemwe 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 18we 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 · 100% = 31.25%