A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number (pure number).

A pie chart showing the percentage by web browser visiting Wikimedia sites (April 2009 to 2012)

Video: Finding a percentage

Examples

For example, 45% (read as "forty-five percent") is equal to ⁴⁵⁄₁₀₀, 45:100, or 0.45. Percentages are often used to express a proportionate part of a total.

(Similarly, one can express a number as a fraction of 1,000 using the term "per mille" or the symbol "‰".).

Example 1

If 50% of the total number of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male.

Example 2

An increase of $0.15 on a price of $2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is a 6% increase.

While many percentage values are between 0 and 100, there is no mathematical restriction and percentages may take on other values. For example, it is common to refer to 111% or −35%, especially for percent changes and comparisons.

Calculations

The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first compute the ratio ⁵⁰⁄₁₂₅₀ = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.

To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:

⁵⁰⁄₁₀₀ × ⁴⁰⁄₁₀₀ = 0.50 × 0.40 = 0.20 = ²⁰⁄₁₀₀ = 20%.

It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = ²⁵⁄₁₀₀ = 0.25, not ^25%⁄₁₀₀, which actually is ²⁵⁄₁₀₀/100 = 0.0025. A term such as ¹⁰⁰⁄₁₀₀% would also be incorrect, this would be read as 1 percent even if the intent was to say 100%.)

Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.

In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?

We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that ⁶⁰⁄₁₀₀ × ⁵⁄₁₀₀ = ³⁄₁₀₀ or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer: ^3%⁄_10% = ³⁰⁄₁₀₀ or 30% of all computer science majors are female.

Percentage increase and decrease

Video: How to Find the Percentage Increase or Decrease of a Number

Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%).

Some other examples of percent changes:

An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial); in other words, the quantity has doubled.
An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
A decrease of 60% means the final amount is 40% of the original (100% – 60% = 40%).
A decrease of 100% means the final amount is zero (100% – 100% = 0%).