Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


gives the number of radians in one degree. It has a numerical value of .


Background & Context
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.
Introduced in 1988
| Updated in 1999