Degree symbol

This article describes the typographical or mathematical symbol. For other meanings, see Degree (disambiguation).
°
Degree symbol
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The degree symbol (°; Unicode: U+00B0, HTML: °) is a typographical symbol that is used, among other things, to represent degrees of arc (e.g. in Geographic coordinate systems) or degrees of temperature. The symbol consists of a small raised circle, historically a zero glyph.

Contents

History

The first recorded modern use of the degree symbol in mathematics is from 1569[1] where the usage clearly shows that the symbol is a small raised zero, to match the symbols for minute, second, third, i.e. prime ′ (U+2032), double prime ″ (U+2033) and triple prime ‴ (U+2034), which originate as small raised Roman numerals for 1, 2, 3. Even finer subdivisions of degrees are also possible, though not common.

Typography

In the case of degrees of arc, the degree symbol follows the number without any intervening space.

In the case of degrees of temperature, two scientific and engineering standards bodies (BIPM and the U.S. Government Printing Office) prescribe printing temperatures with a space between the number and the degree symbol, as in 10 °C.[2][3] However, in many works with professional typesetting, including scientific works published by the University of Chicago Press or Oxford University Press, the degree symbol is printed with no spaces between the number, the symbol, and the Latin letters "C" or "F" representing Celsius or Fahrenheit, respectively (as in 10°C).[4] This is also the practice of the University Corporation for Atmospheric Research, which operates the National Center for Atmospheric Research.[5] Others put a space between the degree symbol and the letter (10° C), which is probably no longer recommended by any of the major style guides. Use of the degree symbol to refer to temperatures measured in kelvins (symbol: K) was abolished in 1967 by the 13th General Conference on Weights and Measures (CGPM). Therefore, the freezing point of water, for instance, is correctly written today as simply 273.15 K. The SI fundamental temperature unit is now "kelvin" (note the lower case), and no longer "degree Kelvin".

Encoding

The degree character was missing from the basic 7-bit ASCII set of 1963, but was introduced in the 1987 Latin-1 extension.

The Unicode code point is U+00B0 (176 decimal), and the code point in CP437 etc is 0xF8 (248 decimal). The HTML entity is °.

Unicode characters similar in appearance include the "masculine ordinal indicator" (U+00BA, º ), the "ring above" combining diacritic (U+02DA, ˚ ), "superscript zero" (U+2070, ⁰ ) and the "ring operator" (U+2218, ∘ ).

There are additional Unicode code points for "Degree Celsius" (U+2103, ℃ ) and "Degree Fahrenheit" (U+2109, ℉ ).

Keyboard entry

Some computer keyboard layouts, such as the QWERTZ layout as used in Germany, Austria and Switzerland, and the AZERTY layout as used in France and Belgium, have the degree symbol available directly on a key. But the common keyboard layouts in English-speaking countries do not include the degree sign, which then has to be input some other way. The method of inputting depends on the operating system being used.

In the Mac OS operating system, the degree symbol can be entered by typing <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">⌥ Opt</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">⇧ Shift</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">8</kbd>. One can also use the Mac OS character palette, which is available in many programs by selecting Special Characters from the Edit Menu, or from the Input Menu (flag) icon on the menu bar (enabled in the International section of the System Preferences).

In Microsoft Windows, one can type <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">Alt</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">2</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">4</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">8</kbd> or <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">Alt</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">0</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">1</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">7</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">6</kbd>, or one can use the Character Map tool to obtain a graphical menu of symbols. In Microsoft Office and similar programs, there is often also an Insert menu with an Insert Symbol or Symbol command that brings up a graphical palette of symbols to insert, including the degree symbol.

In LaTeX, the packages gensymb or textcomp that provides the commands \degree or \textdegree, respectively. In the absence of these packages one can write the degree symbol as ^{\circ} in math mode. In other words, it is written as the empty circle glyph \circ as a superscript.

In Linux operating systems, such as Ubuntu, one can enter Unicode characters in any text entry field by first pressing <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">Ctrl</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">⇧ Shift</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">U</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">Unicode</kbd>. For the degree symbol, this is done by entering <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">Ctrl</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">⇧ Shift</kbd>+<kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">U</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">B</kbd><kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">0</kbd>. Alternatively, the Compose key followed by <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">o</kbd>, <kbd class="keyboard-key" style="border: 1px solid; border-color: #ddd #bbb #bbb #ddd; border-bottom-width: 2px; -moz-border-radius: 3px; -webkit-border-radius: 3px; border-radius: 3px; background-color: #f9f9f9; padding: 1px 3px; font-family: inherit; font-size: 0.85em; white-space: nowrap;">o</kbd> will write the degree symbol.

References

  1. ^ *Cajori, Florian (1993) [1928-1929], A History of Mathematical Notations, Dover Publications, ISBN 0486677664 
  2. ^ The International System of Units (8th ed.), Bureau International des Poids et Mesures, 2006, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 
  3. ^ Style Manual (30th ed.), United States Government Printing Office, 2008, http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=2008_style_manual&docid=f:chapter10.pdf 
  4. ^ (– Scholar search) Chicago Manual of Style (15th ed.), 2006, http://www.chicagomanualofstyle.org/home. 
  5. ^ UCAR, UCAR Communications Style Guide, http://www.ucar.edu/communications/styleguide/d.shtml, retrieved 2007-09-01 

See also

External links