Subscript and superscript - AbsoluteAstronomy.com

A subscript or superscript is a number

Number

A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

, figure, symbol

Symbol

A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...

, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline

Baseline (typography)

In European and West Asian typography and penmanship, the baseline is the line upon which most letters "sit" and below which descenders extend.In the example to the right, the letter 'p' has a descender; the other letters sit on the baseline....

, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formula

Formula

In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....

s, mathematical expression

Expression (mathematics)

In mathematics, an expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Symbols can designate numbers , variables, operations, functions, and other mathematical symbols, as well as punctuation, symbols of grouping, and other syntactic...

s, and descriptions of chemical compound

Chemical compound

A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

s or isotopes, but have many other uses as well.

In professional typography

Typography

Typography is the art and technique of arranging type in order to make language visible. The arrangement of type involves the selection of typefaces, point size, line length, leading , adjusting the spaces between groups of letters and adjusting the space between pairs of letters...

, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually similar to the rest of the font, typeface designers make them slightly heavier than a reduced-size character would be. Likewise, the amount that sub- or superscripted text is moved from the original baseline varies by typeface and by use.

In typesetting, such types are traditionally called superior and inferior letters, figures, etc., or just superiors and inferiors. In English, most non-technical use of superiors is archaic. Superior and inferior figures on the baseline are used for fractions and most other purposes, while lowered inferior figures are needed for chemical and mathematical subscripts.

Uses

A single typeface may contain sub- and super-script glyphs at different positions for different uses. The four most common positions are listed here. Because each position is used in different contexts, not all alphanumerics may be available in all positions. For example, subscript letters on the baseline are quite rare, and many typefaces only provide a limited number of superscripted letters. Despite these differences, all reduced-sized glyphs go by the same generic name of subscript and superscript. Note that the terms subscript and superscript are synonymous with the terms inferior letter (or number) and superior letter (or number), respectively.

Subscripts that are dropped below the baseline

Perhaps the most familiar example of subscripts is in chemical formula

Chemical formula

A chemical formula or molecular formula is a way of expressing information about the atoms that constitute a particular chemical compound....

s. For example, the formula for glucose

Glucose

Glucose is a simple sugar and an important carbohydrate in biology. Cells use it as the primary source of energy and a metabolic intermediate...

is C

Carbon

Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

₆H

Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

₁₂O

Oxygen

Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

₆ (meaning that it is a molecule with 6 carbon

Carbon

atoms, 12 hydrogen

Hydrogen

atoms and 6 oxygen

Oxygen

atoms).

A subscript can also distinguish between different versions of a subatomic particle

Subatomic particle

In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...

. Thus electron, muon, and tau neutrino

Neutrino

A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

s are denoted and . A particle may be distinguished by multiple subscripts, such as for the triple bottom omega particle.

Similarly, subscripts are also used frequently in mathematics to define different versions of the same variable; for example, in an equation x₀ and x_f may indicate the initial and final value of x, while v_rocket and v_observer would stand for the velocities of a rocket and an observer. Commonly, variables with a zero in the subscript are referred to as the variable name followed by "naught". (e.g. v₀ would be read, "v-naught")

Subscripts are often used to refer to members in a mathematical sequence

Sequence

In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...

or set. For example, in the sequence O = (45, -2, 800), O₃ refers to the third member of sequence O, which is 800.

Also in mathematics and computing, subscript can be used to represent the radix

Radix

In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...

, or base, of a written number, especially where multiple bases are used alongside each other. For example, comparing values in hexadecimal

Hexadecimal

In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...

, denary, and octal

Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

one might write C_hex = 12_dec = 14_oct.

Subscripted numbers dropped below the baseline are also used for the denominators of stacked fraction

Fraction (mathematics)

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...

s, like this:

Subscripts that are aligned with the baseline

The only common use of these subscripts is for the denominators of diagonal fraction

Fraction (mathematics)

s, like ½ or the signs for percent %, permille

Permille

A per mil or per mille is a tenth of a percent or one part per thousand. It is written with the sign ‰ , which looks like a percent sign with an extra zero at the end...

‰, and basis point

Basis point

A basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...

. Certain standard abbreviations are also composed as diagonal fractions, such as (care of), (account of), (addressed to the subject), or in Spanish (cada uno/a, "each one").

Superscripts that typically do not extend above the ascender line

These superscripts typically share a baseline with numerator digits, the top of which are aligned with the top of the full-height numerals of the base font; lower-case ascenders may extend above.

Ordinal indicator

Ordinal indicator

In written languages, an ordinal indicator is a sign adjacent to a numeral denoting that it is an ordinal number, rather than a cardinal number. The exact sign used varies in different languages.- English :...

s are sometimes written as superscripts (1^st, 2^nd, 3^rd rather than 1st, 2nd, 3rd), although many English-language style guide

Style guide

A style guide or style manual is a set of standards for the writing and design of documents, either for general use or for a specific publication, organization or field...

s recommend against this use. Other languages use a similar convention, such as 1^er or 2^e in French, or 4ª and 4º in Italian, Portuguese, and Spanish.

Many abbreviation

Abbreviation

An abbreviation is a shortened form of a word or phrase. Usually, but not always, it consists of a letter or group of letters taken from the word or phrase...

s use superscripts, especially historically. Examples in English include J^os and W^m (for Joseph and William), y^e (for the, originally þ

Thorn (letter)

Thorn or þorn , is a letter in the Old English, Old Norse, and Icelandic alphabets, as well as some dialects of Middle English. It was also used in medieval Scandinavia, but was later replaced with the digraph th. The letter originated from the rune in the Elder Fuþark, called thorn in the...

e), th^t or y^t (that), y^r (your), or ma^ty (majesty). In handwritten shorthand, many abbreviations are still written this way, such as defⁿ (definition), exp^t (experiment), or gov^t (government). In French, superscript abbreviations are still quite common, such as M^lle (for Mademoiselle) and G^le (for générale). The standard abbreviation for “number,” №, also uses a superscript. In early modern writing, two-letter abbreviations were sometimes written with the superscript directly above the base letter, as in or .

In early Middle High German

Middle High German

Middle High German , abbreviated MHG , is the term used for the period in the history of the German language between 1050 and 1350. It is preceded by Old High German and followed by Early New High German...

, umlauts and other modifications to pronunciation would be indicated by superscript letters placed directly above the letter they modified. Thus the modern umlaut ü was written as ; both vowel and consonants were used in this way, as in or . In modern typefaces, these letters are usually smaller than other superscripts, and their baseline is slightly above the base font’s midline, making them extend no higher than a typical ordinal indicator.

Superscripts are used for the standard abbreviations for service mark

Service mark

A service mark or servicemark is a trademark used in some countries, notably the United States, to identify a service rather than a product. When a service mark is federally registered, the standard registration symbol ® or "Reg U.S. Pat & TM Off" may be used...

℠ and trademark

Trademark

A trademark, trade mark, or trade-mark is a distinctive sign or indicator used by an individual, business organization, or other legal entity to identify that the products or services to consumers with which the trademark appears originate from a unique source, and to distinguish its products or...

™. The signs for copyright

Copyright is a legal concept, enacted by most governments, giving the creator of an original work exclusive rights to it, usually for a limited time...

© and registered trademark ® are also sometimes superscripted, depending on the use or the typeface.

On hand-written documents and signs, a monetary amount may be written with the cents value superscripted, as in $8 or 8€. Often the superscripted numbers will be underlined: $8, 8€. The currency sign

Currency sign

A currency sign is a graphic symbol used as a shorthand for a currency's name, especially in reference to amounts of money. They typically employ the first letter or character of the currency, sometimes with minor changes such as ligatures or overlaid vertical or horizontal bars...

itself may also be superscripted, as in ^$80 or 6^¢.

Superscripted numerals are used for the numerators of diagonal fraction

Fraction (mathematics)

s, like ¾ or the signs for percent %, permille

Permille

A per mil or per mille is a tenth of a percent or one part per thousand. It is written with the sign ‰ , which looks like a percent sign with an extra zero at the end...

‰, and basis point

Basis point

A basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...

. Certain standard abbreviations are also composed as diagonal fractions, such as (care of), (account of), (addressed to the subject), or in Spanish (cada uno/a, "each one").

Superscripts that typically extend above the ascender line

Both low and high superscripts can be used to indicate the presence of a footnote

Footnote

A note is a string of text placed at the bottom of a page in a book or document or at the end of a text. The note can provide an author's comments on the main text or citations of a reference work in support of the text, or both...

in a document, like this⁵ or this.^xi Any combination of characters can be used for this purpose; in technical writing footnotes are sometimes composed of letters and numbers together, like this.^A.2 The choice of low or high alignment depends on one’s taste, but high-set footnotes tend to be more common, as they stand out more from the text.

In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, high superscripts are used to indicate that one number or variable is raised to the power of another number or variable. Thus y⁴ is y raised to the fourth power, 2^x is 2 raised to the power of x, and the famous equation E = mc² includes a term for the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

squared.

The charges of ion

Ion

An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s and subatomic particle

Subatomic particle

s are also denoted with superscripts. is a negatively charged chlorine

Chlorine

Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

atom, is an atom of lead

Lead

Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

with a charge of positive four, is an electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

, is a positron

Positron

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

, and is an antimuon.

Atomic isotope

Isotope

Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

s are written using superscripts. In symbolic form, the number of nucleons is denoted as a superscripted prefix to the chemical symbol

Chemical symbol

A chemical symbol is a 1- or 2-letter internationally agreed code for a chemical element, usually derived from the name of the element, often in Latin. Only the first letter is capitalised...

(for example , , , , and ). The letters m or f may follow the number to indicate metastable or fission isomer

Nuclear isomer

A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons . "Metastable" refers to the fact that these excited states have half-lives more than 100 to 1000 times the half-lives of the other possible excited nuclear states...

s, as in or .

Subscripts and superscripts can also be used together to give more specific information about nuclide

Nuclide

A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....

s. For example, denotes an atom of uranium

Uranium

Uranium is a silvery-white metallic chemical element in the actinide series of the periodic table, with atomic number 92. It is assigned the chemical symbol U. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons...

with 235 nucleons, 92 of which are protons. A chemical symbol can be completely surrounded: is an ion of carbon

Carbon

with 14 nucleons, of which six are protons and 8 are neutrons.

The numerators of stacked fraction

Fraction (mathematics)

s (such as

) usually use high-set superscripts, although some specially designed glyphs keep the top of the numerator aligned with the top of the full-height numerals.

Alignment examples

This image shows the four common locations for subscripts and superscripts, according to their typical uses. The typeface is Minion

Minion (typeface)

Minion is the name of a typeface designed by Robert Slimbach in 1990 for Adobe Systems. The name comes from the traditional naming system for type sizes, in which minion is between nonpareil and brevier...

Pro, set in Adobe Illustrator. Note that the default superscripting algorithms of most word processors would set the “th” and “lle” too high, and the weight of all the subscript and superscript glyphs would be too light.

Desktop publishing

Many text editing and word processing programs have automatic subscripting and superscripting features, although these programs usually simply use ordinary characters reduced in size and moved up or down – they are not true subscript or superscript glyphs. Professional typesetting programs such as QuarkXPress

QuarkXPress

QuarkXPress is a computer application for creating and editing complex page layouts in a WYSIWYG environment. It runs on Mac OS X and Windows. It was first released by Quark, Inc...

or Adobe InDesign

Adobe InDesign

Adobe InDesign is a software application produced by Adobe Systems. It can be used to create works such as posters, flyers, brochures, magazines, newspapers and books. In conjunction with Adobe Digital Publishing Suite InDesign can publish content suitable for tablet devices...

also have similar features for automatically converting regular type to subscript or superscript. These programs, however, may also offer native OpenType support for the special subscript and superscript glyphs included in many professional typeface packages (such as those shown in the image above). See also OpenType, below.

Comparison of software support
Software	OpenType support for professional glyphs?	Default values for glyph transformation (non-professional glyphs)				Keyboard Shortcuts
Software	OpenType support for professional glyphs?	size	subscript position	superscript position	user-modifiable settings?	subscript	superscript
OpenOffice 2.3	no	58%	-33%	+33%	yes	CTRL+SHIFT+b	CTRL+SHIFT+p
Microsoft Word Microsoft Word Microsoft Word is a word processor designed by Microsoft. It was first released in 1983 under the name Multi-Tool Word for Xenix systems. Subsequent versions were later written for several other platforms including IBM PCs running DOS , the Apple Macintosh , the AT&T Unix PC , Atari ST , SCO UNIX,... 2002	no	65%	-14.1%	+35%	manual¹	CTRL+=	CTRL+SHIFT+=
Adobe Illustrator Adobe Illustrator Adobe Illustrator is a vector graphics editor developed and marketed by Adobe Systems. Illustrator is similar in scope, intended market, and functionality to its competitors, CorelDraw, Xara Designer Pro and Macromedia FreeHand.... CS3	yes	58.3%	-33.3%	+33.3%	yes
Adobe Photoshop Adobe Photoshop Adobe Photoshop is a graphics editing program developed and published by Adobe Systems Incorporated.Adobe's 2003 "Creative Suite" rebranding led to Adobe Photoshop 8's renaming to Adobe Photoshop CS. Thus, Adobe Photoshop CS5 is the 12th major release of Adobe Photoshop... CS3	ordinal letters only	58.3%	-33.3%	+33.3%	manual¹	ALT+CTRL+SHIFT+=	CTRL+SHIFT+=
Notes: 1. Default subscript and superscript options can be overcome by manually changing the font size and raising/lowering text.

HTML subscripts and superscripts
X⁶ O₈M	X⁶O₈M
Default subscript and superscript rendered in HTML for fonts in normal styles.	Example of possible collision of italic styles in HTML.

Position adjustment in italic/oblique/slanted styles

Another subtle adjustment that is most often forgotten in renderers, is controlling the direction of movement for superscripts and subscripts, when they don't lie on the baseline. It should notably take into account the current font's style for italics, notably its slanting direction; most renderers only adjust the position vertically, and forget to shift it horizontally as well. This creates collision with surrounding letters in the same italic size. One can see an example of such collision on the right side when rendered in HTML. To avoid such problem, it is often necessary to insert a small positive horizontal margin (or a thin space) (on the left side of the first the superscript character), or a negative margin (or a tiny backspace) before the subscript. It is more critical with glyphs from fonts in "Oblique" styles that are more slanted than those from fonts in Italic style, and some fonts reverse the direction of slanting, so there's no general solution except when the renderer takes into account the font metrics properties that provides the angle of slanting,

But more generally, the same problem occurs as well between spans of normal glyphs (non-subperscript and non-subscripts) when slanting styles are mixed.

HTML

In HTML and Wiki syntax, subscript text is produced by putting it inside the tags <sub> and </sub>. Similarly, superscripts are produced with and . The exact size and position of the resulting characters will vary by font and browser, but are usually reduced to around 75% original size. Note that superscripts are usually placed too high for many typographic purposes.

TeX

In TeX

TeX

TeX is a typesetting system designed and mostly written by Donald Knuth and released in 1978. Within the typesetting system, its name is formatted as ....

's mathematics mode (as used in MediaWiki

MediaWiki

MediaWiki is a popular free web-based wiki software application. Developed by the Wikimedia Foundation, it is used to run all of its projects, including Wikipedia, Wiktionary and Wikinews. Numerous other wikis around the world also use it to power their websites...

), subscripts are typeset with the underscore

Underscore

The underscore [ _ ] is a character that originally appeared on the typewriter and was primarily used to underline words...

, while superscripts are made with the caret

Caret

Caret usually refers to the spacing symbol ^ in ASCII and other character sets. In Unicode, however, the corresponding character is , whereas the Unicode character named caret is actually a similar but lowered symbol: ....

. Thus $X_{ab}$ produces

, and $X^{ab}$ produces

Unicode

Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...

defines subscript and superscript characters in several areas, in particular it has a full set of superscript and subscript digits. Due to the popularity of using these characters to make fractions, most modern fonts render most or all of these as cap height superscripts and baseline subscripts. The same font may align letters and numbers in different ways. Other than numbers, the set of super- and subscript letters and other symbols is incomplete and somewhat random, and many fonts do not contain them. Because of these inconsistencies, these glyphs may not be suitable for some purposes (see Uses, above).

OpenType

One of the advanced features of OpenType typefaces is support for professionally designed subscript and superscript glyphs. Exactly which glyphs are included varies by typeface; some have only basic support for numerals, while others contain a full set of letters, numerals, and punctuation. Since many of these glyphs are not included in Unicode, they are typically placed in the Unicode Private Use Area.

External links

Vincent Connare’s type-design standards for Microsoft
Vertical alignment questions from Typophile
Typophile (Internet forum)
Typophile is an internet forum hosted at www.Typophile.com dedicated to the discussion of type, typefaces, fonts and typography and the associated software, tools and design practices of people who work with type...

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.