Percentage Calculator

Please provide any two values below and click the "Calculate" button to get the third value.

Percentage Calculator in Common Phrases

Percentage Difference Calculator

Percentage Change Calculator

Please provide any two values below and click the "Calculate" button to get the third value.

What is a percentage?

In mathematicsa percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratiosfractionsand decimals. Percentages are often denoted by the symbol "%" written after the number. They can also be denoted by writing "percent" or "pct" after the number. For example35% is equivalent to the decimal 0.35or the fractions .

Percentages are computed by multiplying the value of a ratio by 100. For exampleif 25 out of 50 students in a classroom are male. The value of the ratio is therefore 0.5and multiplying this by 100 yields:

0.5 × 100 = 50

In other wordsthe ratio of 25 males to students in the classroom is equivalent to 50% of students in the classroom being male.

Percentage formula

Although the percentage formula can be written in different formsit is essentially an algebraic equation involving three values.

P × V₁ = V₂

P is the percentageV₁ is the first value that the percentage will modifyand V₂ is the result of the percentage operating on V₁. The calculator provided automatically converts the input percentage into a decimal to compute the solution. Howeverif solving for the percentagethe value returned will be the actual percentagenot its decimal representation.

EX: P × 30 = 1.5

If solving manuallythe formula requires the percentage in decimal formso the solution for P needs to be multiplied by 100 in order to convert it to a percent. This is essentially what the calculator above doesexcept that it accepts inputs in percent rather than decimal form.

Percentage difference formula

The percentage difference between two values is calculated by dividing the absolute value of the difference between two numbers by the average of those two numbers. Multiplying the result by 100 will yield the solution in percentrather than decimal form. Refer to the equation below for clarification.

Percentage change formula

Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematicallythis involves using the absolute value of the difference between two values then dividing the result by the initial valueessentially calculating how much the initial value has changed.

The percentage increase calculator above computes an increase or decrease of a specific percentage of the input number. It basically involves converting a percent into its decimal equivalentand either subtracting (decrease) or adding (increase) the decimal equivalent from and to 1respectively. Multiplying the original number by this value will result in either an increase or decrease of the number by the given percent. Refer to the example below for clarification.

EX: 500 increased by 10% (0.1)
500 × (1 + 0.1) = 550

500 decreased by 10%
500 × (1 – 0.1) = 450