Percent Calculator for
Calculating Missing Percentage Variable

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The Percent Calculator on this page will calculate a percentage of a number as well as calculate numbers from percentages.

This free online percentage calculator can calculate percentages the following three different ways.

1. What percentage is one number of another number.

2. What unknown number is a given percentage of another number.

3. What unknown number is a given number a given percentage of.

Plus, unlike other online percentage calculators, this percent calculator allows you to choose the decimal rounding, explains how it arrived at the given result, and shows a visual representation of the result in a pie chart.

How to Calculate Percentages

Besides using the percent calculator on this page, there are basically two different ways to calculate percentages: Using a shortcut method, and using a proportion method.

There are also two general uses for percent calculations: Calculating a percentage from numbers, and calculating numbers from a percentage. To explain how to calculate percentages I will cover both methods for each use. But first let's make sure you aware of the conversion concepts you need to know in order to solve for unknown percentage variables.

Percent Conversions

The first thing you need to be aware of when calculating percentages is that a percentage (p) can be rewritten as the fraction p/100. In other words, 25% can be rewritten as 25/100. And since 25 ÷ 100 is equal to .25, you can see that a percentage can either be converted to a fraction or a decimal. The actual conversion you will need to make will depend on whether you are using the shortcut method or the proportion method.

Number Conversions

The second thing you need to be aware of when calculating percentages, is that the numbers needed to calculate percentages (n and d) can also be rewritten as the fraction n/d, where n is a relationship or ratio to d. For example, if you are trying to find out what percentage 5 is of the number 20, this can be expressed as 5/20. And since 5 ÷ 20 = .25, you can see that the numbers themselves can be expressed as either a fraction or a decimal. Again, the actual conversion you will need to make depends on the method you use to solve for the unknown variable.

Keeping those conversion concepts in mind, let's take a look at each method to show you how to calculate percentages from number, and then how to calculate an unknown number from a number and a percentage.

How to Calculate a Percentage from Two Numbers

To find what percentage a first number is of a second number, the shortcut method is to simply divide the first number (numerator) by the second number (denominator). This will yield a decimal number, which can then be converted into a percentage.

To convert a decimal into a percentage you can either multiply the decimal by 100, or simply move the decimal point two places to the right.

The following is an example of how you would calculate what percent 45 is of 180 using the shortcut method:

Shortcut Method to Solve for Percentage

p = 45
180

p = .25

Convert decimal to percent:

p = .25 * 100

p = 25%

Or, you can formulate the problem into a proportion and then solve for the missing percentage. Here is how you would solve for the above example using the proportion method:

Formulate a Proportion and Solve for Percentage

45 = p
180 100

Cross multiply:

45 * 100 = 180 * p

4500 = 180p

Divide both sides by 180

4500 = 180p
180 180

25 = p

25/100 = .25 or 25%

How to Calculate a Number from a Percentage and a Number

If you know the percentage and one of the needed numbers, you can find the unknown number using either the shortcut method or the proportion method. Since n/d (45/180 in our example) represents the two numbers needed to find a percentage, I'll refer to n as the numerator and d as the denominator.

Now, since the formula to find a number from a percentage and a number depends on whether or not you are trying to find the first number (n or numerator) or the second number (d or denominator), I'll explain each formula separately.

How to Calculate the Numerator Given the Percentage and the Denominator

If you are trying to find the first number (numerator), the shortcut method is to convert the percentage into a decimal and then multiply that decimal by the second number (denominator).

The following is an example of how you would calculate what number (n) is 25% of 180 using the shortcut method:

Shortcut Method to Solve for Numerator

n = 25%
180

Convert percent to decimal:

25% = .25

Multiply decimal by denominator:

n = .25 * 180:

n = 45

Or, you can formulate a proportion and use cross multiplication to solve for the numerator. Here is how you would solve for the numerator in the above example using the proportion method:

Formulate a Proportion and Solve for Numerator

n = 25
180 100

Cross multiply:

n * 100 = 180 * 25

100n = 4500

Divide both sides by 100

100n = 4500
100 100

n = 45

How to Calculate the Denominator Given the Percentage and the Numerator

If you are trying to find the second number (denominator), you simply divide the first number by the decimal equivalent of the percentage.

The following is an example of how you would calculate what number (d) that 45 is 25% of using the shortcut method:

Shortcut Method to Solve for Denominator

45 = 25%
d

Convert percent to decimal:

25% = .25

Divide the numerator by the decimal:

d = 45 ÷ .25

d = 180

Or, you can formulate a proportion and use cross multiplication to solve for the denominator. Here is how you would solve for the denominator in the above example using the proportion method:

Formulate a Proportion and Solve for Denominator

45 = 25
d 100

Cross multiply:

45 * 100 = d * 25

4500 = 25d

Divide both sides by 25

4500 = 25d
25 25

180 = d

Finally, if we combine all three findings using the same example, we end up with the following statement:

The number 45 is 25% of the number 180

- or -

The number n is p% of the number d

The above explains why I set up the percent calculator the way I did. You can enter any two of the above underlined variables and the calculator will find the third variable.

With that, let's use the percent calculator to solve for a number or a percentage.

Percent Calculator
Calcy sign introducing Percent Calculator


Instructions: Enter any two of the three percentage variables and then click the "Calculate Percentage" button.

Mouse over the blue question marks for a further explanation of each entry field or button. More in-depth explanations can be found in the glossary of terms located beneath the Percent Calculator.

Help Number of decimal places to round result to:
Help The number is % of the number
Help Raw result (no rounding):

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Percent Calculator Glossary of Terms

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Percentage: A numerical expression indicating how one number compares to another. For example, to numerically express what portion 5 people represent out of a group of 20 people (5/20), the 5 people would represent 25% of the group (5/20 = .25, or 25%).

Proportion: A method that uses cross multiplication for solving for an unknown variable in an equation involving percentages or ratios. A proportion a/b = c/d is equal to the cross multiplication ad = bc.

Number of decimal places to round result to: Select how many decimal places you would like the result rounded to. Note that the percent calculator will always give the raw result in the field provided, and then use the rounded version for the result explanation and the pie chart.

The number __ is __% of the number __: Fill in two of the three fields depending on which solution you are looking for. The empty field will be completed by the percent calculator after clicking the Calculate Percentage button.

Raw result (no rounding): This is the un-rounded version of the rounding per your selection at the top of percent calculator.

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