# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Pi

Pi
is , with numerical value .

## Background & ContextBackground & Context

• Pi is the symbol representing the mathematical constant , which can also be input as . Pi is defined as the ratio of the circumference of a circle to its diameter and has numerical value . Pi arises in many mathematical computations including trigonometric expressions, special function values, sums, products, and integrals as well as in formulas from a wide range of mathematical and scientific fields.
• When Pi is used as a symbol, it is propagated as an exact quantity. While many expressions involving Pi (e.g. Cos[Pi/10]) are automatically expanded in terms of simpler functions, expansion and simplification of more complicated expressions involving Pi (e.g. Cos[Pi/15]) may require use of functions such as FunctionExpand and FullSimplify.
• Pi 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 it is not known if Pi is normal (meaning the digits in its base- expansion are equally distributed) to any base, its known digits are very uniformly distributed.
• Pi can be evaluated to arbitrary numerical precision by means of the Chudnovsky formula using N. In fact, calculating the first million decimal digits of Pi takes only a fraction of a second on a modern desktop computer. RealDigits can be used to return a list of digits of Pi and ContinuedFraction to obtain terms of its continued fraction expansion.
• Most angle-related functions in the Wolfram Language take radian measures as their arguments and return radian measures as results. The symbol Degree, which is equal to , can therefore be used as a multiplier when entering values in degree measures (e.g. Cos[30 Degree]).

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Pi can be entered as EscpEsc:

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Evaluate to any precision:

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Do an exact numerical computation:

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