A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation. When that angle is with respect to a reference meridian, it indicates a location along a great circle of a sphere, such as Earth (see Geographic coordinate system), Mars, or the celestial sphere.
The degree of a term of a polynomial in one variable is the exponent on the variable in that term; the degree of a polynomial is the highest such degree. For example, in 2x3 + 4x2 + x + 7, the term of highest degree is 2x3; this term, and therefore 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; the degree of the polynomial is again the highest such degree. For example, the polynomial x2y2 + 3x3 + 4y has degree 4, the same degree as the term x2y2.
The degree of an algebraic number is the smallest degree of a non-trivial polynomial in one variable with rational coefficients having said algebraic number as a root. For instance, any rational number is degree 1 since it is the root of the polynomial .
Additionally, the square root of any non-square positive integer, say , is degree 2, as it is the root of .
In graph theory, the degree of a vertex in a graph is the number of edges incident to that vertex — in other words, the number of lines coming out of the point. In a directed graph, the indegree and outdegree count the number of directed edges coming into and out of a vertex respectively.