Percentage Calculator

This calculator can be used to solve the following percentage formula:

y = x · p%

To use the calculator, select the desired form of the equation, provide the values, and click the "Calculate" button.

What is a percentage?

A percentage is a number that is expressed as a fraction of 100, and is denoted using the symbol "%". For example, 12 percent, or 12%, is equivalent to the fraction . A percentage is a dimensionless value, since it represents a part of a whole out of 100 parts. Percentages are commonly used to express some proportion of a total. For example, given that 12 out of every 100 apples (12%) are spoiled, then if John purchases 500 apples, he can expect 60 of the apples to be spoiled, since . When using percentages in this way, they usually range from 0-100%, but percentages do not necessarily have to remain within that range. They can also take on negative values, or values larger than 100, such as in cases discussing percentage change. For example, if John starts with 100 apples, then purchases 150 more, he now has 250 apples, which is 250% of 100.

Percentage formula and calculations

The percentage formula makes use of the equation, y = x · p%. Given this equation, as long as 2 of the values are known, it is possible to use the formula to calculate the third.

For example, given that 80% of students pass the math exam and there are 60 people in the class, how many people will pass the exam? This type of problem involves solving for y in the percentage equation, where p% = 80%, and x = 60:

y = 60 × 80% = 60 × 0.8 = 48

Thus, 48 students will pass the exam.

In the above example, y was the unknown. In other types of problems, either x or p% will be the unknown. For example, if a stadium can seat 70,000 people, and 42,700 people attend an event, what percentage of the stadium is occupied? This type of problem involves solving for p% in the percentage equation, where y = 42,700 and x = 70,000. Rearranging the percentage formula,

Thus, the stadium is 61% occupied.

The final form of the equation involves solving for x. If an item is 70% off and the final sale price is $21, what was the original price of the item? This type of problem involves solving for x in the percentage equation, where y = 21 and p% = 70%. Rearranging the percentage formula,

Thus, the original price of the item was $30.

Converting percentages to fractions or decimals

It can be useful to express percentages in either fraction or decimal form, so knowing how to convert between the three can be helpful.

Percentages and fractions

Converting from a percentage to a fraction is trivial, as we saw above. Given a percentage, simply write the value as the numerator of the fraction, where the denominator is 100, then simplify if possible.

Converting a fraction to a percentage is simple if the fraction can be rewritten as an equivalent fraction out of 100. In cases where this is possible, the numerator of the equivalent fraction out of 100 is the percentage. For example:

In cases where the fraction cannot be written as an equivalent fraction out of 100, perform long division, then multiply the result by 100 and write the final result along with the % symbol:

Percentages and decimals

A percentage represents one hundredth. Thus, . Because of this, to convert from a decimal to a percentage, simply multiply the decimal by 100:

0.723 × 100 = 72.3%

Similarly, to convert a percent to a decimal, simply divide by 100 and remove the % symbol: