Subscript and superscript

Example of subscript and superscript. In each example the first “2” is professionally designed, and is included as part of the glyph set; the second “2” is a manual approximation using a small version of the standard “2.” The visual weight of the first “2” matches the other characters better. (The top typeface is Adobe Garamond Pro; the size of the subscript is about 62% of the original characters, dropped below the baseline by about 16%. The second typeface is Myriad Pro; the superscript is about 60% of the original characters, raised by about 44% above the baseline.)

A subscript or superscript is a number, figure, symbol, or indicator that is smaller than their normal line of type and is set slightly below or above it. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well.

In professional typography, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually consistent with the rest of the font, typeface designers make them slightly heavier than a reduced-size character would be. The distance 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 nontechnical use of superiors is archaic.^[1] 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.^[2]

Uses

The four common locations of subscripts and superscripts. The typeface is Myriad Pro.

A single typeface may contain sub- and superscript 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 provide only a limited number of superscripted letters. Despite these differences, all reduced-size glyphs go by the same generic terms subscript and superscript, which are synonymous with the terms inferior letter (or number) and superior letter (or number), respectively. Most fonts that contain superscript/subscript will have predetermined size and orientation that is dependent on the design of the font.

Subscripts that are dropped below the baseline

Perhaps the most familiar example of subscripts is in chemical formulas. For example, the molecular formula for glucose is C₆H₁₂O₆ (meaning that it is a molecule with 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms).

A subscript is also used to distinguish between different versions of a subatomic particle. Thus electron, muon, and tau neutrinos are denoted ν
e ν
μ and ν
τ. A particle may be distinguished by multiple subscripts, such as Ω−
bbb 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 might 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 “nought” (e.g. v₀ would be read, “v-nought”).

Subscripts are often used to refer to members of a mathematical sequence or set or elements of a vector. 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, a subscript can be used to represent the radix, or base, of a written number, especially where multiple bases are used alongside each other. For example, comparing values in hexadecimal, denary, and octal one might write C_hex = 12_dec = 14_oct.

Subscripted numbers dropped below the baseline are also used for the denominators of stacked fractions, like this: $\tfrac{67}{68}$.

Subscripts that are aligned with the baseline

The only common use of these subscripts is for the denominators of diagonal fractions, like ½ or the signs for percent %, permille ‰, and basis point ‱. 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; lowercase ascenders may extend above.

Ordinal indicators are sometimes written as superscripts (1^st, 2^nd, 3^rd, 4^th, rather than 1st, 2nd, 3rd, 4th), although many English-language style guides recommend against this use.^[3] Other languages use a similar convention, such as 1^er or 2^e in French, or 4ª and 4º in Spanish, Portuguese, Galician and Italian.

In medieval manuscripts, many superscript signs were used to abbreviate text. From these developed modern diacritical marks (accents placed above the letter). Also, in early Middle 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 uͤ; both vowels and consonants were used in this way, as in ſheͨzze or boͮsen.^[4] 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 ℠ and trademark ™. The signs for copyright © and registered trademark ® are also sometimes superscripted, depending on the use or the typeface.

On handwritten documents and signs, a monetary amount may be written with the cents value superscripted, as in $8⁰⁰ or 8€⁵⁰. Often the superscripted numbers are underlined: $8⁰⁰, 8€⁵⁰. The currency symbol itself may also be superscripted, as in ^$80 or 6^¢.

Superscripted numerals are used for the numerators of diagonal fractions, like ¾ or the signs for percent %, permille ‰, and basis point ‱. 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 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 taste, but high-set footnotes tend to be more common, as they stand out more from the text.

In mathematics, 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 squared. This led over time to an “abuse of notation” whereby superscripts indicate iterative function composition, including derivatives. In an unrelated use, superscripts also indicate contravariant tensors in Ricci calculus.

The charges of ions and subatomic particles are also denoted by superscripts. Cl- is a negatively charged chlorine atom, Pb4+ is an atom of lead with a positive charge of four, e− is an electron, e+ is a positron, and μ+ is an antimuon.

Atomic isotopes are written using superscripts. In symbolic form, the number of nucleons is denoted as a superscripted prefix to the chemical symbol (for example 3He, 12C, 13C, 131I, and 238U). The letters m or f may follow the number to indicate metastable or fission isomers, as in 58mCo or 240fPu.

Subscripts and superscripts can also be used together to give more specific information about nuclides. For example, 235
92U denotes an atom of uranium with 235 nucleons, 92 of which are protons. A chemical symbol can be completely surrounded: 14
6C2+
8 is an ion of carbon with 14 nucleons, of which six are protons and 8 are neutrons.

The numerators of stacked fractions (such as $\tfrac{34}{35}$) 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 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.

Position adjustment in italic/oblique/slanted styles

HTML subscripts and superscripts
X^6 O8M	X^6O8M
Default subscript and superscript rendered in HTML for fonts in normal styles.	Example of possible collision of italic styles in HTML.

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 adjust the position only 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 is 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.

Software support

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 or Adobe InDesign 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
		Size	Subscript position	Superscript position	User-modifiable settings?	Superscript	Subscript
OpenOffice.org 3.3	no	58%	−33%	+33%	yes	Ctrl+⇧ Shift+P	Ctrl+⇧ Shift+B
Microsoft Word 2015	yes	50%	−14.1%	+40%	manual^1	Ctrl+⇧ Shift+=	Ctrl+=
Adobe Illustrator CS3	yes	58.3%	−33.3%	+33.3%	yes
Adobe Photoshop CS3	ordinal letters only	58.3%	−33.3%	+33.3%	manual^1	Alt+Ctrl+⇧ Shift+=	Ctrl+⇧ Shift+=
LaTeX	yes (using XeLaTeX only)	≈70%^2	−14%^3	+25%^3	manual^4	math: ^ (caret) text: \textsuperscript{stuff}	math: _ (underscore) text: \textsubscript{stuff}^5
Notes: Default subscript and superscript options can be overcome by manually changing the font size and raising/lowering text. Dependent on math mode; differs for subsub- and supersuper-scripts. Nominal values; dependent on fontdimen parameters (16 and 17). Changing fontdimen values requires some skill (see this thread) but the textual commands can be modified to use the \raisebox command. Requires package fixltx2e.

HTML

In HTML and Wiki syntax, subscript text is produced by putting it inside the tags <sub> and </sub>. Similarly, superscripts are produced with <sup> and </sup>.^[5] 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’s mathematics mode (as used in MediaWiki), subscripts are typeset with the underscore, while superscripts are made with the caret. Thus $X_{ab}$ produces $X_{ab}$, and $X^{ab}$ produces $X^{ab}$.

In LaTeX text mode the math method above is inappropriate, as letters will be in math italic, so the command n\textsuperscript{th} will give n^th and A\textsubscript{base} will give A_base (textual subscripts are rare, so \textsubscript is not built-in, but requires the fixltx2e package). As in other systems, when using UTF-8 encoding, the masculineº and feminineª ordinal indicators can be used as characters, with no need to use a command.

Superscripts and subscripts of arbitrary height can be done with the \raisebox{<dimen>}{<text>} command: the first argument is the amount to raise, and the second is the text; a negative first argument will lower the text. In this case the text is not resized automatically, so a sizing command can be included, e.g. go\raisebox{1ex}{\large home}.

Unicode

Unicode defines subscript and superscript characters in several areas; in particular, it has a full set of superscript and subscript digits. Owing 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.

See also

• Mathematical notation
• Typographical conventions in mathematical formulae
• Superior letter
• Furigana
• Ruby character
• Typesetting
• Font
• Superscripts and Subscripts

References

1. Bringhurst 2005, pp 311–12.
2. Bringhurst 2005, p 309.
3. "UCC EPU: Editing Word files for publication: Making the best of what Word provides". Publish.ucc.ie. 2011-07-03. Retrieved 2014-01-03.
4. http://std.dkuug.dk/JTC1/SC2/WG2/docs/n2266.pdf
5. "Math Unicode Entities". Tlt.its.psu.edu. 2013-06-04. Retrieved 2014-01-03.

Bibliography

• Bringhurst, Robert (2005), The Elements of Typographic Style, 3rd ed., Vancouver: Hartley and Marks, ISBN 0-88179-205-5.

External links

• Vincent Connare’s type-design standards for Microsoft
• Vertical alignment questions from Typophile