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Percentage Calculator: Free Online Instant Calculation

  • Published: 2013-12-12 (Rev. 2016-05-30) - Contact: Ian Langtree at Disabled World
  • Synopsis: Free online instant calculator for finding a percentage of a number as well as reverse percentage calculations.

Main Document

"When speaking of a 10% rise or a 10% fall, the usual interpretation is that this is relative to the initial value of that quantity."

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Percentage is often denoted using the percent sign, "%", or the abbreviation "pct."

It comes from per cent which is short for per centum which means per hundred.

In British English, percent is sometimes written as two words (per cent, although percentage and percentile are written as one word).

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) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%.

NOTE: 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%.)


  • 1 percent (1%) = 1 part per 100 = 1/100 = 0.01 (a portion less than a whole)
  • 100 percent (100%) = 100 parts per 100 = 100/100 = 1 (a portion equal to a whole)
  • 110 percent (110%) = 110 parts per 100 = 110/100 = 1.1 (a portion greater than a whole)

When speaking of a 10% rise or a 10% fall, 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%).

Examples of percent changes:

  • A decrease of 100% means the final amount is zero (100% - 100% = 0%).
  • A decrease of 60% means the final amount is 40% of the original (100% - 60% = 40%).
  • An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
  • 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.

In general, a change of x percent in a quantity results in a final amount that is 100+x percent of the original amount (equivalently, 1+0.01x times the original amount).

Percentage Calculator
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Facts: Percentage History

The term "per cent" is derived from the Latin per centum, meaning "by the hundred".

The sign for "per cent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred".

The "per" was often abbreviated as "p." and eventually disappeared entirely.

The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.


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