{{Short description|Irreducible fraction}} {{for|the computer virus|OneHalf}} {{redirect|Half}} {{Wiktionary|one half}} {{more sources|date=September 2025}} {{Infobox number | number = 0.5 | cardinal = one half | ordinal = {{frac|1|2}}th (halfth) |lang1=Greek |lang1 symbol={{resize|155%|'''∠'''}} |lang2=Roman numerals |lang2 symbol={{resize|125%|'''S'''}} |lang3=Egyptian hieroglyph |lang3 symbol={{resize|250%|'''𓐛'''}} |lang4=Hebrew |lang4 symbol={{resize|125%|חֵצִ}} |lang5=Malayalam |lang5 symbol={{resize|125%|൴}} |lang6=Chinese |lang6 symbol={{resize|125%|半}} |lang7=Tibetan |lang7 symbol={{resize|175%|༪}} }}
'''One half''' is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements.
== As a word == One half is one of the few fractions which are commonly expressed in natural languages by suppletion rather than regular derivation: the word for "half" in various languages is etymologically unrelated to their word for "two". In English, for example, other small fractions, such as "sixth" and "eleventh", are derived from the corresponding number word.
A ''half'' can also be said to be one part of something divided into two equal parts. It is acceptable to write one half as a hyphenated word, ''one-half''.
== Mathematics == One half is the rational number that lies midway between 0 and 1 on the number line. Multiplication by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling".
[[File:Eye of Horus square.png|thumb|175px|A square of side length one, here dissected into rectangles whose areas are successive powers of '''one half'''.]]
A number raised to the power of one half is equal to its square root. This follows from the fact that when multiplying powers, the exponents add. So, <math>a^{1/2}</math> times itself is <math>a^{1/2 + 1/2}</math> which is <math>a^1</math>, which equals <math>a</math>.
The area of a triangle is one half its base and its height, also known as its altitude.<ref>{{cite book|first1=Donna |last1=Kirk |display-authors=etal |year=2024 |isbn=978-1-951693-68-8 |title=Contemporary Mathematics |publisher=OpenStax |chapter=10.6 Area |chapter-url=https://openstax.org/books/contemporary-mathematics/pages/10-6-area}}</ref>[[File:ModularGroup-FundamentalDomain.svg|350px|right|thumb|Fundamental region of the modular ''j-invariant'' in the '''upper half-plane''' (shaded <span style="color: gray;">gray</span>), with modular discriminant <math>|\tau| \ge 1</math> and <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) \le \tfrac{1}{2}</math>, where <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) < 0 \Rightarrow |\tau| > 1.</math> ]]
The gamma function evaluated at one half is the square root of pi.<ref>{{cite book|first=Greg |last=Gbur |author-link=Greg Gbur |title=Mathematical Methods for Optical Physics and Engineering |year=2011 |publisher=Cambridge University Press |isbn=978-0-521-51610-5 |page=776}}</ref>
It has two different decimal representations in base ten, the familiar <math>0.5</math> and the recurring <math>0.4\overline{9}</math>, with a similar pair of expansions in any even base; while in odd bases, one half has no terminating representation.
The Bernoulli number <math>B_{1}</math> has the value <math>\pm \tfrac {1}{2}</math> (its sign depending on competing conventions).<ref>{{cite book |first1=John |last1=Conway |author-link1=John Horton Conway |first2=Richard |last2=Guy |author-link2=Richard K. Guy |title=The Book of Numbers |title-link=The Book of Numbers (math book) |publisher=Springer-Verlag |date=1996 |isbn=0-387-97993-X |page=107}}</ref><ref>{{cite book|last=Arfken |first=George |date=1970 |title=Mathematical methods for physicists |edition=2nd |publisher=Academic Press |bibcode=1970mmp..book.....A |isbn=978-0120598519 |page=278}}</ref>
The Riemann hypothesis is the conjecture that every nontrivial complex root of the Riemann zeta function has a real part equal to <math>\tfrac {1}{2}</math>.<ref>{{cite web|url=https://www.claymath.org/millennium/riemann-hypothesis/ |title=Riemann Hypothesis |website=Clay Mathematics Institute |access-date=2025-09-12}}</ref>
== Computer characters == {{Infobox symbol | align="left" |sign = {{notatypo|½}} |name = vulgar fraction '''one half''' |unicode = {{unichar|00BD}} |see also = {{unichar|00BC|nlink=quarter (disambiguation)}}<br />{{unichar|00BE|nlink=threequarters (disambiguation)}} }}
The "one-half" symbol has its own code point as a precomposed character in the Latin-1 Supplement <!-- Unlike most fractions, NOT in the Number Forms block! --> block of Unicode, rendering as {{char|½}}. <!--Keyboard entry (including alt codes and typewriters) is system- and localisation-specific. It is not the function of Wikipedia to tell readers how to negotiate their own specific configuration. -->
The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment; consequently the decomposed forms {{char|{{frac|2}}}} or {{char|{{sfrac|2}}}} may be more appropriate.
==See also== thumb|160px|right|Postal stamp, Ireland, 1940: one halfpenny postage due. *Division by two
==References== {{Reflist}}
{{Fractions and ratios}}
Half Category:Rational numbers