View source for Overline

{{Short description|Horizontal line immediately above a portion of writing}}
{{hatnote|This article is about the typographic element. For the diacritic, see [[macron (diacritic)]] and [[bar (diacritic)]].}}
{{More citations needed|date=October 2009}}

{| class="wikitable" align="right"
|-
! Description || Sample || Unicode || CSS/HTML
|-
| Overline<br/>(markup)
| {{overline|Xx}} || {{n/a}}
| style="font-size:75%" | <code>text-decoration: overline;</code>
|-
| rowspan="2" | Overline<br/>(character)
| ‾ || U+203E || <code>&amp;oline;</code>, <code>&amp;#8254;</code>
|-
| X&#773;x&#773; <small> (combining)</small> || U+0305 || <code>X&amp;#773;</code> 
|-
| Double overline<br/>(markup)
| <span style="text-decoration:overline;text-decoration-style: double;">Xx</span> || {{n/a}}
| style="font-size:75%" | <code>text-decoration: overline;<br/>&nbsp;text-decoration-style: double;</code>
|-
| Double overline<br/>(character)
| X&#831;x&#831; <small> (combining)</small> || U+033F || <code>X&amp;#831;</code>
|-
| rowspan="3" | Macron<br/>(character)
| ¯ || U+00AF || <code>&amp;macr;</code>, <code>&amp;#175;</code>
|-
| X&#772;x&#772; <small> (combining)</small> || U+0304 || <code>X&amp;#772;</code>
|-
| X̄x̄ <small> (precomposed)</small>
| colspan="2" style="background: #ececec; color: #2C2C2C; vertical-align: middle; text-align: {{{align|center}}} | varies
|}
An '''overline''', '''overscore''', or '''overbar''', is a [[typographical]] feature of a [[horizontal and vertical|horizontal]] line drawn immediately above the text. In old [[mathematical notation]], an overline was called a ''[[vinculum (symbol)|vinculum]]'', a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign. The original use in [[Ancient Greek]] was to indicate compositions of [[Greek alphabet|Greek letters]] as [[Greek numerals]].<ref>Smith, T. P. (2013). ''How Big is Big and How Small is Small: The Sizes of Everything and Why''.</ref> In Latin, it indicates [[Roman numeral]]s multiplied by a thousand and it forms medieval abbreviations ([[sigla]]). Marking one or more words with a continuous line above the characters is sometimes called ''[[overstriking]]'', though overstriking generally refers to printing one character on top of an already-printed character.

An overline, that is, a single line above a chunk of text, should not be confused with the [[macron (diacritic)|macron]], a [[diacritical mark]] placed above (or sometimes below) ''individual'' letters. The macron is narrower than the character box.<ref name="Wells">{{cite web | url=http://www.phon.ucl.ac.uk/home/wells/dia/diacritics-revised.htm#macron | title=Orthographic diacritics and multilingual computing | publisher=[[University College London]] | date=2001 | access-date=23 March 2014 | author=Wells, J.C. | author-link=John C. Wells }}</ref>

==Uses==

===Medicine===
{{main|scribal abbreviation|medical abbreviation|macron (diacritic)}}
In most forms of [[Latin language|Latin]] [[scribal abbreviation]], an overline or [[macron (symbol)|macron]] indicates omitted letters similar to use of [[apostrophe]]s in English contractions. Letters with macrons or overlines continue to be used in [[medical abbreviation]]s in various European languages, particularly for [[medical prescription|prescriptions]]. Common examples include

* '''{{overline|a}}''', '''a&#773;''', or '''ā''' for {{lang|la|{{linktext|ante}}}} ("before")
* '''{{overline|c}}''', '''c&#773;''', or '''c̄''' for {{lang|la|{{linktext|cum}}}} ("with")
* '''{{overline|p}}''', '''p&#773;''', or '''p̄''' for {{lang|la|{{linktext|post}}}} ("after")<ref>{{Cite book|title=Manuali Hoepli Lexicon Abbreviature Dizionario Di Abbreviature Latine ed Italiane|last=Cappelli|first=Adriano|publisher=Editore Ulrico Hoepli Milano|year=1961|location=Milan|pages=256}}</ref>
* '''{{overline|q}}''', '''q&#773;''', or '''q̄''' for {{lang|la|{{linktext|quisque}}}} and its inflections ("every", "each")
* '''{{overline|s}}''', '''s&#773;''', or '''s̄''' for {{lang|la|{{linktext|sine}}}} ("without")
* '''{{overline|x}}''', '''x&#773;''', or '''x̄''' for {{lang|la|{{linktext|exceptus}}}} and its inflections ("except")

Note, however, that abbreviations involving the letter h take their macron halfway up the ascending line rather than at the normal height for Unicode overlines and macrons: [[ħ]]. This is separately encoded in [[Unicode]] with the symbols using [[bar diacritic]]s and appears shorter than other overlines in many fonts.

===Math and science===
====Decimal separator====
{{Main|Decimal separator}}
In the [[Middle Ages]], from the original [[Hindu-Arabic numeral system|Indian decimal writing]], before printing, an overline over the [[units digit]] was used to separate the integral part of a number from its [[fractional part]], as in 9{{overline|9}}95 (meaning 99.95 in decimal point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 99<sup>{{underline|95}}</sup>.{{fact|date=January 2022}}

====Vinculum====
In mathematics, an overline can be used as a [[vinculum (symbol)|vinculum]].

The vinculum can indicate a [[line segment]]:<ref>{{Cite web|title=Line Segment Definition - Math Open Reference| url=https://www.mathopenref.com/linesegment.html|access-date=2020-08-24|website=www.mathopenref.com}}</ref><math display="block">\overline{\rm AB}</math>The vinculum can indicate a [[repeating decimal]] value: <math display="block">{1\over7} = 0.\overline{142857}=0.142857142857142857142857...</math> When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: <math display="block">3.\overline{\phantom{I}}3=3.\overline{3}=3.3333333333333333333333333...</math>
<math display="block">3.12\overline{\phantom{I}}34 = 3.12\overline{34}=3.123434343434343434343434...</math>
Historically, the vinculum was used to group together symbols so that they could be treated as a unit. Today, parentheses are more commonly used for this purpose.

====Statistics====
The overline is used to indicate a [[sample mean]]:<ref>{{Cite web|title=Sample Means|url=http://www.stat.yale.edu/Courses/1997-98/101/sampmn.htm|access-date=2020-08-24|website=www.stat.yale.edu}}</ref>
*<math>\overline x</math> is the average value of <math>x_i</math>

[[Survival function]]s or complementary cumulative distribution functions are often denoted by placing an overline over the symbol for the cumulative: <math>\overline{F}(x) =1-F(x)</math>.

====Negation====
In [[set theory]] and some [[electrical engineering]] contexts, [[negation]] operators (also known as [[Complement (set theory)|complement]]) can be written as an overline above the term or expression to be negated.<ref>{{Cite web|title=Set Operations {{!}} Union {{!}} Intersection {{!}} Complement {{!}} Difference {{!}} Mutually Exclusive {{!}} Partitions {{!}} De Morgan's Law {{!}} Distributive Law {{!}} Cartesian Product|url=https://www.probabilitycourse.com/chapter1/1_2_2_set_operations.php|access-date=2020-08-24|website=www.probabilitycourse.com}}</ref> For example:

Common set theory notation:
:<math>\begin{align}
  \overline{A \cup B} &\equiv \overline{A} \cap \overline{B} \\
  \overline{A \cap B} &\equiv \overline{A} \cup \overline{B}
\end{align}</math>

Electrical engineering notation:
:<math>\begin{align}
  \overline{A \cdot B} &\equiv \overline {A} + \overline {B} \\
      \overline{A + B} &\equiv \overline {A} \cdot \overline {B}
\end{align}</math>
in which the times (cross) means multiplication, the dot means logical AND, and the plus sign means logical OR.

Both illustrate [[De Morgan's laws]] and its mnemonic, "break the line, change the sign".

====Negative====
In [[common logarithms]], a bar over the characteristic indicates that it is negative—whilst the mantissa remains positive. This notation avoids the need for separate tables to convert positive and negative logarithms back to their original numbers.

:<math>\log_{10}0.012\approx-2+0.07918=\bar{2}.07918</math>

====Complex numbers====
The overline notation can indicate a [[complex conjugate]] and analogous operations.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Complex Conjugate|url=https://mathworld.wolfram.com/ComplexConjugate.html|access-date=2020-08-24|website=mathworld.wolfram.com|language=en}}</ref>
*if <math>x = a + ib</math>, then <math>\overline{x} = a - ib.</math>

====Vector====
In physics, an overline sometimes indicates a [[Euclidean vector|vector]], although [[boldface]] and [[arrow (symbol)|arrows]] are also commonly used:
*<math>\overline x = |x|\hat x</math>

====Congruence classes {{Anchor|Residue|Residue class|Congruence class}}====
Congruence modulo {{math|''n''}} is an [[equivalence relation]], and the [[equivalence class]] of the integer {{math|''a''}}, denoted by {{math|{{overline|''a''}}{{sub|''n''}}}}, is the set {{math|{... , ''a'' − 2''n'', ''a'' − ''n'', ''a'', ''a'' + ''n'', ''a'' + 2''n'', ...}}}. This set, consisting of all the integers congruent to {{math|''a''}}&nbsp;modulo&nbsp;{{math|''n''}}, is called the '''congruence class''', '''[[modular arithmetic|residue class]]''', or simply '''residue''' of the integer {{math|''a''}} modulo&nbsp;{{math|''n''}}. When the modulus {{math|''n''}} is known from the context, that residue may also be denoted {{math|[''a'']}} or {{math|{{overline|''a''}}}}.

====Topological closure====
In [[topology]], the [[closure (topology)|closure]] of a subset ''S'' of a [[topological space]] is often denoted {{math|{{overline|''S''}}}} or <math>\operatorname{cl} S</math>.

====Improper rotation====
In [[crystallography]], an overline indicates an [[improper rotation]] or a [[negative number]]:
*<math>\overline 3</math> is the [[Hermann–Mauguin notation]] for a threefold rotoinversion, used in [[crystallography]].
*<math>[\overline 11\overline2]</math> is the direction with [[Miller index|Miller indices]] <math>h=-1</math>, <math>k=1</math>, <math>l=-2</math>.

====Maximal conductance====
In [[computational neuroscience]], an overline is used to indicate the "maximal" conductances in [[Hodgkin-Huxley model]]s. This goes back to at least the landmark paper published by Nobel prize winners [[Alan Lloyd Hodgkin]] and [[Andrew Fielding Huxley]] around 1952.<ref name="HH">{{Cite journal 
| last1 = Hodgkin | first1 = A. L. 
| last2 = Huxley | first2 = A. F. 
| title = A quantitative description of membrane current and its application to conduction and excitation in nerve 
| journal = The Journal of Physiology 
| volume = 117 
| issue = 4 
| pages = 500–544 
| year = 1952 
| pmid = 12991237 
| pmc = 1392413
 | doi=10.1113/jphysiol.1952.sp004764
}}</ref>

: <math>I_\mathrm{Na}(t)=\bar{g}_\mathrm{Na} m(V_m)^3h(V_m)(V_m-E_\mathrm{Na})</math>

====Antiparticles====
Overlines are used in subatomic particle physics to [[Antimatter#Notation|denote antiparticles]] for some particles (with the alternate being distinguishing based on electric charge). For example, the [[proton]] is denoted as {{Subatomic particle|proton}}, and [[Antiproton|its corresponding antiparticle]] is denoted as {{Subatomic particle|antiproton}}.

=== Engineering ===
An [[active low]] signal is designated by an overline, e.g. {{overline|RESET}}, [[#Negation|representing logical negation]].

=== Graphics Design ===
Overlining is also used in graphics design for decoration of text to help convey a message.<ref name="Overline vs: Underline: Unraveling the Differences">{{cite web | url=https://fastercapital.com/content/Overline-vs--Underline--Unraveling-the-Differences.html | title=Overline vs: Underline: Unraveling the Differences | publisher=Faster Capital | date=18 June 2024 | accessdate=8 September 2024}}</ref>

=== Morse (CW) ===
Some Morse code [[Prosigns for Morse code|prosigns]] can be expressed as two or three characters run together, and an overline is often used to signify this. The most famous is the [[SOS|distress signal]], {{overline|SOS}}.

===Writing===
An overline-like symbol is traditionally used in [[Syriac language|Syriac]] text to mark abbreviations and numbers. It has dots at each end and the center. In German it is occasionally used to indicate a pair of letters which cannot both be fitted into the available space.<ref>{{cite web|last1=Hardwig|first1=Florian|title=Gräfinnen|url=https://www.flickr.com/photos/hardwig/6388399531/|website=Flickr|access-date=26 December 2017|date=2011-11-23}}</ref><ref name="Lieder zur Weihnachtszeit">{{cite web|last1=Hardwig|first1=Florian|title=Lieder zur Weihnachtszeit (1940)|url=https://fontsinuse.com/uses/11409/lieder-zur-weihnachtszeit-1940|website=Fonts in Use|access-date=26 December 2017|quote=It used to be common to mark omitted double letters with an overbar, especially for "mm" and "nn". These abbreviations come in handy when lyrics have to match the musical notes, see 'da kom[m]t er her'.|date=2015-12-26}}</ref>

When [[Morse code]] is written out as text, overlines are used to distinguish [[prosigns for Morse code|prosigns]] and other concatenated character groups from strings of individual characters.

In [[Arabic typography|Arabic writing and printing]], overlines are traditionally used instead of [[Underline|underlines]] for [[Emphasis (typography)|typographic emphasis]],<ref>{{Cite web|title=Emphasis (typography)|url=https://graficnotes.blogspot.com/2016/08/emphasis-typography.html|access-date=2020-09-02|website=Emphasis (typography)}}</ref> although underlines are used more and more due to the rise of the internet.
[[File:Persian_Bible_overline.png|alt=Overlines used in a version of the Bible in Persian (1920)|thumb|300x300px|Overlines used in a version of the [[Bible]] in [[Persian language|Persian]] (1920)]]

===Linguistics===
[[X-bar theory]] makes use of overbar notation to indicate differing levels of [[syntactic structure]]. Certain structures are represented by adding an overbar to the unit, as in {{overline|X}}. Due to difficulty in typesetting the overbar, the [[prime symbol]] is often used instead, as in X{{prime}}. Contemporary typesetting software, such as LaTeX, has [[#TeX|made typesetting overbars considerably simpler]]; both prime and overbar markers are accepted usages. Some variants of X-bar notation use a double-bar (or double-prime) to represent phrasal-level units.

X-bar theory derives its name from the overbar. One of the core proposals of the theory was the creation of an intermediate syntactic node between phrasal (XP) and unit (X) levels; rather than introduce a different label, the intermediate unit was marked with a bar.

==Implementations==

===HTML with CSS===

In [[HTML]] using [[Cascading Style Sheets|CSS]], overline is implemented via the [[text decoration|text-decoration]] property; for example, <code><nowiki><span style="text-decoration: overline">text</span></nowiki></code> results in: {{overline|text}}.

The text decoration property supports also other typographical features with horizontal lines: [[underline]] (a line {{underline|below}} the text) and [[strikethrough]] (a line {{strikethrough|through}} the text).

===Unicode===

Unicode includes two [[graphic character]]s, {{unichar|00AF|macron}} and {{unichar|203E|overline}}. They are [[Unicode equivalence|compatibility equivalent]] to the {{unichar|0020|space|nlink=space (punctuation)}} with non-spacing diacritics {{unichar|0304|combining macron|cwith=◌|nlink=macron (diacritic)}} and {{unichar|0305|combining overline|cwith=◌}} respectively; the latter allows an overline to be placed over any character. There is also {{unichar|033F|combining double overline|cwith=◌}}. As with any [[combining character]], it appears in the same character box as the character that logically precedes it: for example, x̅, compared to x‾. A series of overlined characters, for example 1̅2̅3̅, may result either in a broken or an unbroken line, depending on the font.

In Unicode, character {{mono|U+FE26}} {{smallcaps2|1=COMBINING CONJOINING MACRON}} is conjoining (bridging) two characters: {{mono|1={{big|1=◌&#xFE26;◌}}}}.

In East Asian ([[CJK]]) computing, {{unichar|FFE3|fullwidth macron}} is available. Despite the name, Unicode maps this character to both U+203E and U+00AF.<ref name="UnicodeFull"/>

Unicode maps the overline-like character from [[ISO/IEC 8859-1]] and [[code page 850]] to the {{unichar|00AF|macron}} symbol mentioned above. In a reversal of its official name (and compatibility decomposition), it is much wider than an actual macron diacritic over most letters, and actually wider than {{unichar|203E|overline}} in most fonts. In [[ChromeOS]] and [[Linux]], the symbol can be added using the keystrokes {{keypress|Ctrl|Shift|U}} to activate [[Unicode input]], then type "00AF" as the code for the character. On a [[Mac (computer)|Mac]], with the <code>ABC Extended</code> keyboard, use {{keypress|Option|a}}. In [[Microsoft Windows]], U+00AF can be entered with the keystrokes {{key press|Alt|0}}{{key press|1|7|5|chain=}} (where numbers are entered from the [[numeric keypad]]).

The Unicode character {{unichar|070F|Syriac Abbreviation Mark|nlink=}} is used to mark [[#Writing|Syriac abbreviations and numbers]]. However, several computer environments do not render this line correctly or at all.

The Unicode character {{unichar|0B55|ORIYA SIGN OVERLINE}} is used as a length mark in [[Odia script]].

===Word processors===
[[Collabora Online]], an office suite for the web has direct menu support for several styles of Overline in the "Format" menu, with options available under "Format > Character" enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set.

[[Collabora Online|Collabora Office]] and [[LibreOffice]]
have direct menu support for several styles of Overline in the "Format" menu. The user-interface option is available in their word processors on Linux, macOS and Windows, and also in Android (in tablet format), ChromeOS and iPadOS with Collabora Office. Options for Overline are available under the menu: "Format > Character", enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set.

[[Microsoft Word]] does not have a menu option to edit Overlining in Microsoft Word for any operating system, or in Word for the web. Overlining can be added using fields codes, <code>EQ \O()</code>. The field code <code>{EQ \O(x,¯)}</code> produces {{overline|x}} and the field code <code>{EQ \O(xyz,¯¯¯)}</code> produces {{overline|xyz}}; However this does not work in Word on Android, ChromeOS, iPadOS, or Word for the web. In Word 2010 it is necessary to insert an MS Equation object.

Overstriking of longer sections of text, such as in {{overline|123}}, can also be produced in many [[word processing|text processors]] as [[markup language|text markup]] as a special form of understriking.

===Spreadsheet, Presentation and Graphics office suite applications===
[[Collabora Online]], [[Collabora Online|Collabora Office]] and [[LibreOffice]] have direct menu support for several styles of Overline in the "Format" menu within applications of their office suites, including spreadsheets, presentations and graphics applications. The user-interface option is available in  the web based suite, and the locally installable applications for Linux, macOS and Windows, and with Collabora Office in Android (in tablet format), ChromeOS and iPadOS. Options for Overline are available under the menu: "Format > Character", enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set.

===TeX===<!--caution: an internal #-link -->
In [[LaTeX]], a text <text> can be overlined with <code>$\overline{\mbox{<text>}}$</code>. The inner <code>\mbox{}</code> is necessary to
override the math-mode (here invoked by the dollar signs) which the <code>\overline{}</code> demands.

== See also ==
{{Commons category|Overlining}}
* [[Ā]]
* [[Titlo]], an overline used to indicate numerals or abbreviations in Cyrillic
* [[Underscore]]

==References==
<references>
<ref name="UnicodeFull">{{Citation
 | chapter-url = https://www.unicode.org/charts/PDF/UFF00.pdf
 | chapter =Halfwidth and Fullwidth Forms
 | title = The Unicode Standard 6.1
 | author = The Unicode Consortium
 | year= 2012
 | publisher =Unicode Consortium
 | isbn = 978-1-936213-02-3
 | quote = FULLWIDTH MACRON • sometimes treated as fullwidth overline
}}</ref>
</references>

[[Category:Typography]]
[[Category:Punctuation]]
[[Category:Ancient Greek punctuation]]