Percentage Calculator Online

This calculator allows you to calculate the percentage of a number online. It uses 5 basic formulas for finding percentages in all possible situations, from the simplest task of calculating a percentage value of a given number, to the more complex cases of using percentages.

Directions for Use

To use the percent calculator, choose the calculation type from the drop-down menu. The drop-down menu items are grouped based on the formulas used for the calculations. However, you don’t need to know the exact formula to be able to use it.

There is a list of questions under each formula that covers the most common percentage calculations. The questions are formulated as self-explanatory, so choosing the relevant question is obvious.

For example, if you need to calculate a sum of a value and a 50% share of the same value, such as (5 + 50% of 5), you simply have to find the relevant question. In the case of the above example, the question will be, “X plus P% is WHAT?” You will immediately see that this question is in the group of the following formula X + (X × P%) = Y, which means that you will use this formula to solve the problem.

After choosing the appropriate question, enter the known values in the corresponding fields. For the above example (5 + 50% of 5), you would enter 5 in the X field and 50 in the P field. Then press “Calculate.” The calculator will display the answer and the detailed solution of the problem using the relevant formula.

Definitions

The percentage is a relative value used to define a share in relation to a whole. “The whole,” or the initial value, is defined as 100%, while a hundredth share of that whole is defined as 1%. Twice the initial value would be 200%.

For example, if you have a hundred cookies, then 1 cookie would be 1%, 150 cookies would be 150%, and 200 cookies would be 200%. Similarly, if you have 50 cookies, 1% would be the one-hundredth share of 50, i.e., 50 / 100 = 0.5. So, 1% of 50 cookies is half a cookie. While 100 cookies would be 50 + 50, i.e., 100% + 100% = 200%.

Calculating Percentages

The above definition is commonly used to find percentages of numbers. To find 1% of any number, simply divide the number by 100: 1% of x is always x / 100.

To find any percentage y of a number x, multiply the value for 1% with y.

For example, to find 20% of x:

y = 20

20% of x = (x / 100) × 20

Percentage Proportion

The following proportion is often used to find the percentage of a number if the whole number is known:

$$\frac{Whole\ number}{Percentage} = \frac{100\%}{y\%}$$

For example, to find 10% of 75, the proportion would be written as follows:

$$\frac{75}{x} = \frac{100\%}{10\%}$$

To find the value of x, the above proportion is solved for x:

$$x=\frac{(75×10\%)}{100\%}=7.5$$

10% of 75 = 7.5

Percentage Proportion for Reversed Calculations

The percentage proportion can also be used for reversed calculations to answer questions like this: what percentage of 20 is 5? In this case, 20 is 100%, and 5 is y%, i.e.

$$\frac{20}{5} = \frac{100\%}{y\%}$$

Solving for y, we get:

$$y=\frac{(5×100\%)}{20}=25\%$$

The answer is: 5 is 25% of 20.

Decimal Expression of Percentages

Percentage values are often expressed as decimals. To find a decimal value of percentage, divide by 100:

10% = 10 / 100 = 0.1

25% = 25 / 100 = 0.25

The proportion described above can also be expressed in decimals. To find a percentage of a number, multiply the number by the decimal expression of the necessary percentage. For the example above, to find 10% of 75, multiply 75 by 0.1 to get 7.5:

10% of 75 = 75 × (10 / 100) = 75 × 0.1 = 7.5

Calculation Example – Calculating Tips

Calculating tips is one of the most common usages of percentage in everyday life. Imagine you went to a restaurant and spent $32 on a meal. You would like to add a 15% tip. So, what is 15% of $32?

Solution

Use the proportion formula described above to find 15% of $32. You will get the following proportion:

$$\frac{32}{x} = \frac{100\%}{15\%}$$

$$x=\frac{(32×15\%)}{100\%}=4.8$$

Or,

15% from 32 = 32 × (15 / 100) = 32 × 0.15 = 4.8

First, choose the appropriate question from the drop-down menu to use the online percentage calculator to solve this problem. In this example, the question will be, “WHAT is P% of X?” The known values are P = 15 and X = 32.

After pressing “Calculate, the calculator will display the answer (4.8) and the detailed solution.

Calculating the total bill

The calculator also allows you to calculate the total bill you would pay in this case. To calculate the total bill in this example, you need to answer the following question: What is $32 + 15% of $32?

The corresponding question from the drop-down menu is: “X plus P% is WHAT?” The known values are X = 32 and P = 15.

After pressing “Calculate” you will see the final answer: 36.8, the detailed solution to the problem, and the value of the added 15%.

The total bill equals $32 + $4.8 = $36.8

Calculation Example – Calculating Discounts

To calculate the discount price of an item, you need to know the original price and the discount percentage. Let’s find a discount price for a t-shirt if the original price was $16, and it is currently on sale with a 20% discount.

Solution

Let’s first find the 20% of $16. Let’s use the decimal expression of percentage this time:

20% of $16 = $16 × (20 / 100) = $16 × 0.2 = $3.2

To perform this operation, using the online calculator choose the following question: “WHAT is P% of X?” Enter the known values for P and X: P = 20 and X = 16.

After pressing “Calculate,” the calculator will display the final answer: 3.2, and the solution to the problem.

To find the discount price, subtract the discount from the original price:

$16 - $3.2 = $12.8

Calculating the Final Price

The calculator also allows you to calculate the resulting discount price of the t-shirt immediately. To do that, choose the following question from the drop-down list: “X minus P% is WHAT?” Enter the known numbers: X = 16 and P = 20.

After pressing “Calculate,” the calculator will display the final answer: 12.8, followed by the detailed solution.