# 5.5 `math` -- Mathematical functions

This module is always available. It provides access to the mathematical functions defined by the C standard.

These functions cannot be used with complex numbers; use the functions of the same name from the `cmath` module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don't is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number used as a parameter, so that the programmer can determine how and why it was generated in the first place.

The following functions are provided by this module. Except when explicitly noted otherwise, all return values are floats:

`acos`( | x)

  Return the arc cosine of x.

`asin`( | x)

  Return the arc sine of x.

`atan`( | x)

  Return the arc tangent of x.

`atan2`( | y, x)

  Return `atan(y / x)`.

`ceil`( | x)

  Return the ceiling of x as a float.

`cos`( | x)

  Return the cosine of x.

`cosh`( | x)

  Return the hyperbolic cosine of x.

`degrees`( | x)

  Converts angle x from radians to degrees.

`exp`( | x)

  Return `e**x`.

`fabs`( | x)

  Return the absolute value of x.

`floor`( | x)

  Return the floor of x as a float.

`fmod`( | x, y)

  Return `fmod(x, y)`, as defined by the platform C library. Note that the Python expression `x % y` may not return the same result.

`frexp`( | x)

  Return the mantissa and exponent of x as the pair `(m, e)`. m is a float and e is an integer such that `x == m * 2**e`. If x is zero, returns `(0.0, 0)`, otherwise `0.5 <= abs(m) < 1`.

`hypot`( | x, y)

  Return the Euclidean distance, `sqrt(x*x + y*y)`.

`ldexp`( | x, i)

  Return `x * (2**i)`.

`log`( | x[, base])

  Returns the logarithm of x to the given base. If the base is not specified, returns the natural logarithm of x. Changed in version 2.3: base argument added.

`log10`( | x)

  Return the base-10 logarithm of x.

`modf`( | x)

  Return the fractional and integer parts of x. Both results carry the sign of x. The integer part is returned as a float.

`pow`( | x, y)

  Return `x**y`.

`radians`( | x)

  Converts angle x from degrees to radians.

`sin`( | x)

  Return the sine of x.

`sinh`( | x)

  Return the hyperbolic sine of x.

`sqrt`( | x)

  Return the square root of x.

`tan`( | x)

  Return the tangent of x.

`tanh`( | x)

  Return the hyperbolic tangent of x.

Note that `frexp()` and `modf()` have a different call/return pattern than their C equivalents: they take a single argument and return a pair of values, rather than returning their second return value through an `output parameter' (there is no such thing in Python).

The module also defines two mathematical constants:

`pi`
  The mathematical constant pi.

`e`
  The mathematical constant e.

Note: The `math` module consists mostly of thin wrappers around the platform C math library functions. Behavior in exceptional cases is loosely specified by the C standards, and Python inherits much of its math-function error-reporting behavior from the platform C implementation. As a result, the specific exceptions raised in error cases (and even whether some arguments are considered to be exceptional at all) are not defined in any useful cross-platform or cross-release way. For example, whether `math.log(0)` returns `-Inf` or raises `ValueError` or `OverflowError` isn't defined, and in cases where `math.log(0)` raises `OverflowError`, `math.log(0L)` may raise `ValueError` instead.

See Also:

Module `cmath`:
  Complex number versions of many of these functions.