Besides using the percent calculator on this site, there are basically two different ways to calculate percentages:
- Using a shortcut method.
- Using a proportion method.
There are also two general uses for percent calculations:
- Calculating a percentage from numbers.
- 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 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 a 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:
| 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:
| 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:
| 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:
| 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) 45 is 25% of, using the shortcut method:
| 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:
| 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:
- 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.