Per cent

of unit
name per cent
of dimension unity
character %
symbol p
designated after lat. per cento
(on one hundred [referred])
from unity see
derived also: Parts per thousand

number data in per cent (of one hundred, of lat. per = up, in; centum = one hundred, in a general manner: Hundredths) serve thatIllustration and the comparable making of quantitative proportions, in which they are always set to the same basic value, i.e. one hundred, in relationship. Percentage figures are marked by the symbol %: 22.5%

in computer science are used this indication (purpose-alienated) usually for the operation modulo.

In legal texts usesone usually the expressions „of one hundred “(shortened: front spar) and „per cent point “. DIN recommends however to avoid these expressions.

Table of contents

to definition

a per cent is the hundredth part of a whole one thus: 1% = 0.01

according to DIN 5477 from February 1983 the numerical value can with” the indication of quotients of numbers or sizes of same dimension including the money “by splitting the factor 10 -2 off to be transformed; here the factor 10 -2 the character % is named. This indication is to be spoken per cent or hundredths.


percentage figures a similar function as the formulations „a half “, „a third “etc. fulfill, howevercan they very many more differentiated quantitative proportions express, e.g. „22.5 of 100 “= 22.5 per cent.

In order to be able to understand percentage figures, one must know on which the indication refers and on the basis the grammatical expression the used arithmetic rules to derive to be able.

base factor of percentage figures

data inPer cent, like e.g.a probability of rain of 30% “ or a relative risk reduction of 25% “, are understandable only if the base factor (which are „100% “?) one indicates.

An example is the computation of the value added tax. This is defined by the value of a product () Multiplies net by the VAT rate. The sum of the net amount and the value added tax results in the gross amount:

Gross amount = net amount + value added tax
gross amount = net amount + (net amount ∙ VAT rate)

are 100 euro the net amount and the VAT rate amount to 20% (as in Austria), thuscalculates one the value added tax through:

∙ euro or 100 euro ∙ 20

0.01 = 20 euro the gross amount is therefore calculated

100 euro for 20% = 20:

100 euro + 20 euro = 120 euro

the linguistic usage in practice

  • „inInvoice amount are 20% value added tax “means

that the VAT rate amounts to 20% and the invoice amount the gross amount is, thus net amount contained plus 20% value added tax. Correctly it would have to read therefore: „In the invoice amount the value added tax (with a VAT rate of 20%) is “„

  • the value added tax amounts to contained20% “

wrong, should actually are called „ the VAT rate amount to 20% “.

  • „20% of the invoice amount are value added tax “

wrong, if the VAT rate amounts to 20%, since it acts with the invoice amount around the net value plus value added tax. Are from an amount from for example 120 euro 20%equivalent 24 euro. The contained value added tax amounts to actual however 20 euro and constitutes approximately 16.667% of the invoice amount here.

The expressions „over “and „up “are to be differentiated:

  • „My content rose by 5 per cent and the rent around 3 per cent sunk “

means the samelike

  • „my content to 105 per cent and the rent rose to 97 per cent sunk “

also these data is meaningfully only if the basic value admits is, to which the percentage figure refers, e.g. „… in the comparison to the previous year “.

conversion between payment and percentages

The expression „50% of the whole one “contains the same information as the expression „0.5 of the whole one “. One converts the numerical value 0.5 by multiplication with 100 into the percentage.


in mathematics of finance the symbol p is divided in this formula by 100.Thus one wants to build the conversion directly into the formula. Mathematically regarded this is however a calculation error during the transformation within a system of units and is not SI-Komform (see conversion between payment and percentages). The sum of all percentages p x must here always 1 (100%) result in; The sum of all percentages W x results in the basic value:

<math> {{\ sum_ {x} p_x} = 1} {,} \, {{\ sum_ {x} W_x} = G}< /math>

input at the pocket calculator

pocket calculator of different design and manufacturer treat the keyboard entry of a calculation of percentage differently and usually even wrongly. This can to confusionlead and/or. to the fact that users of pocket calculators do with Prozentrechnungungen without the percent key and rather to the three-set falls back.

see also

Wiktionary: Per cent - word origin, synonyms and translations

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