Degree
gives the number of radians in one degree. It has a numerical value of 
.
Details
- You can multiply by Degree to convert from degrees to radians, so that 30Degree represents 30°.
- Degree can be entered in StandardForm and InputForm as °,
deg
or \[Degree]. - Degree is printed in StandardForm as °.
Background & Context
- Degree is the symbol representing the number of radians in one angular degree (1°), which can also be input into the Wolfram Language as ∖[Degree]. Degree has exact value
and numerical value 
. The use of Degree is especially common in calculations involving plane geometry and trigonometry. While most angle-related functions in the Wolfram Language take radian measures as their arguments and return radian measures as results, the symbol Degree can be used as a multiplier when entering values in degree measures (e.g. Cos[30 Degree]). - When Degree is used as a symbol, it is propagated as an exact quantity that can be expressed in terms of Pi using FunctionExpand. While many expressions involving Degree (e.g. Cos[30 Degree]) are automatically expanded in terms of simpler functions, expansion and simplification of more complicated expressions involving Degree (e.g. Cos[12 Degree]) may require use of functions such as FunctionExpand and FullSimplify.
- As a result of its close relationship with Pi, Degree is known to be both irrational and transcendental, meaning it can be expressed neither as a ratio of integers nor as the root of any integer polynomial. While (like Pi) it is not known if Degree is normal (meaning the digits in its base-
expansion are equally distributed) to any base, its known digits are very uniformly distributed. - Degree can be evaluated to arbitrary numerical precision using N. In fact, calculating the first million decimal digits of Degree takes only a fraction of a second on a modern desktop computer due to the rapid convergence of the Chudnovsky formula for Pi. RealDigits can be used to return a list of digits of Degree and ContinuedFraction to obtain terms of its continued fraction expansion.
- Note that the Wolfram Language unit framework represents the angular degree as Quantity[1,"AngularDegrees"] for the purposes of unit encoding and conversion. Some care is therefore needed in distinguishing the mathematical constant Degree (which relates degrees to radians) and the unit of angular measure itself. This slightly unfortunate dual nature of degrees has its roots in the treatment of angular measure by the SI system of units, which treats radians as a dimensionless measure whose explicit specification is optional.
Examples
open allclose allBasic Examples (3)
Use in arguments of trigonometric functions:
Degree can be entered as 
deg
:
Properties & Relations (4)
Evaluate symbolic relations involving Degree:
Use FullSimplify to simplify expressions containing Degree:
Degree is not an algebraic number:
Radians may be converted to degrees using UnitConvert and Quantity as well as Degree:
Possible Issues (1)
Degree is typically not generated as output:
FullSimplify does not transform expressions to Degree:
Text
Wolfram Research (1988), Degree, Wolfram Language function, https://reference.wolfram.com/language/ref/Degree.html (updated 2002).
CMS
Wolfram Language. 1988. "Degree." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2002. https://reference.wolfram.com/language/ref/Degree.html.
APA
Wolfram Language. (1988). Degree. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Degree.html