# Degree

A

**degree** is the name of several

units of measurement, and also an academic qualification.

### Angle

A **degree of arc**, usually symbolized by the symbol °, 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. Where degree measures are used, you'll also find minutes (one-60th of a degree, or 1/21600 of the way around, symbolized by a single quotation mark) and seconds (one-60ths of a minute, or 1/1296000 of the way around , symbolized by a double quotation mark). Thus 40°12'13" is 40 degrees, 12 minutes, 13 seconds, or about 11/100 of the way around.

In more mathematical context, angles are usually measured in radians instead of degrees. One degree equals π/180 radians.

There was also an attempt to introduce a decimal degree, see gon.

Several units of measuring temperature. The symbol is usually ° followed by the initial letter, for example ° C.

Note that the

SI unit of temperature, the

kelvin, uses the symbol

*K* and is not proceeded by "degrees" or the degree sign (°).

A "degree of freedom" is a concept in mathematics,

physics and

engineering. See the article "

degrees of freedom" for the use of this concept.

The **degree** of a term of a polynomial is the exponent on the variable in that term; the degree of an entire polynomial is the degree of the term of highest degree. For example, the term of highest degree in 2*x*^{3} + 4*x*^{2} + *x* + 7 is 2*x*^{3}; this term, and therfore the entire polynomial, are said to have degree 3. For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term, and the degree of a polynomial is again the degree of the term of highest degree. For example, the degree of the polynomial *x*^{2}*y*^{2} + 3*x*^{3} + 4*y* is 4, the degree of the *x*^{2}*y*^{2} term.

In graph theory, the **degree** of a vertex of a graph is the number of edges incident to that vertex.

A **degree** is an award conferred on a person by an institution of higher education, generally in recognition of academic achievement, but in some cases merely as a honor for non-academic work (the later are called honorary degrees, or degrees *honoris causa*). A person issued a degree is permitted to place initials after their name indicating the award, and in some cases (Doctorates and Higher Doctorates) assume the title of Doctor (by custom people with doctorates honoris causa do not assume this title).
See also: Academic degrees: B.A, M.Sc, M.A, MBA, M.D, J.D, Ph.D, D.A, D.M.A, Ed.D, D.M.L, D.Sc

The term is used to specify levels of burns, ranging from first degree burns to third degree burns.

In music or

music theory a

**scale degree** is an individual

note of a

scale. First,

second,

third,

fourth,

fifth,

sixth, and

seventh may be used to indicate degree as well as

tonic,

supertonic,

mediant,

subdominant,

dominant,

submediant,

subtonic, and

leading tone. The degree sign "°" is used to indicate that a

chord is

diminished. The chord built upon a the fifth scale degree, or dominant, with also be called the fifth or dominant chord.