Degree

This article describes "degree" as a unit of measurement. For alternative meanings, see Degree (disambiguation).

Angle

A degree of arc, usually symbolized by the symbol &deg, is a measurement of plane angles, or of a location along a great circle of a sphere (such as the Earth or the celestial sphere); it represents going one-360th the way around the circumference of a circle or sphere.

The number 360 was probably chosen because it is divisible by 24 positive integers, including every number from 1 to 10 except 7. (For the number of degrees in a circle to be divisible by every number from 1 to 10, there would need to be 2520 degrees in a circle, which is a much less convenient number).

Often, where degree measures are used, one also finds minutes (representing 1/60th of a degree of arc and symbolized by a single quotation mark or a prime symbol) and seconds (1/60th of a minute, or 1/3600th of a degree, and symbolized by a double quotation mark or double-prime symbol). For example, 40.20361° is frequently represented as 40°12'13" or 40 degrees, 12 minutes, 13 seconds. It is common to use these smaller units of measurement when giving the latitude and longitude of a location on the Earth.

Because the notion that there are 360 degrees in a circle is an artificial concept, more rooted in number theory than in geometry, mathematicians typically prefer to use radians, because the number of radians in an angle corresponds to the number of radii that equal the arc length of the angle. Because there are 2π radii around the circumferance of a circle, 360° equals 2π radians, so 1° = π/180 rad ≈ 0.0174533 rad; and 1 rad = 360°/(2π) = 180°/π ≈ 57.29578°.

With the invention of the metric system, based on powers of ten, there was an attempt to define a "decimal degree" (grad or gon), so that the number of decimal degrees in a right angle would be 100, and there would be 400 decimal degrees in a circle. This idea did not gain momentum.

Temperature

The term degree is used in several scales of temperature. The symbol ° is usually used, followed by the initial letter of the unit, for example ° C for degrees Celsius.

• degrees Celsius (° C)
• degrees Fahrenheit (° F)
• degrees Rankine
• degrees Réaumur

Note that the metric unit of temperature, the kelvin, uses the symbol K (always capitalized) and is not preceded by "degrees" nor the degree sign (°).

For comparison, at sea level pure water freezes at 0° C, 32° F or 273.15 K. Similarly at sea level pure water boils at 100° C, 212° F or 373.15 K.

For temperature differences, the usage is reversed: 100 C° (read "Celsius degrees") is a temperature difference, while 100° C is an actual temperature. Hence the difference between the boiling and freezing points of water is 100 C° or 180 F°.

Degree symbol

In Unicode, the "degree sign" is U+00B0 (°). The HTML code for it is °.

Due to a similar appearance in some fonts in print and on computer screens, some other characters may be mistakenly substituted for it: the "masculine ordinal indicator" (U+00BA, º), the "ring above" (U+02DA, ˚), "superscript zero" (U+2070, ⁰), superscript zero proper (⁰) or superscript letter "o" (^o), and the "ring operator" (U+2218, ∘).