This manual page is part of the POSIX Programmer's Manual. The Linux
implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior), or
the interface may not be implemented on Linux.
The functionality described on this reference page is aligned with
the ISO C standard. Any conflict between the requirements described
here and the ISO C standard is unintentional. This volume of
POSIX.1‐2008 defers to the ISO C standard.
These functions shall compute the principal value of the arc tangent
of y/x, using the signs of both arguments to determine the quadrant
of the return value.
An application wishing to check for error situations should set errno
to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
functions. On return, if errno is non-zero or fetestexcept(FE_INVALID
| FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error
Upon successful completion, these functions shall return the arc
tangent of y/x in the range [−π,π] radians.
If y is ±0 and x is < 0, ±π shall be returned.
If y is ±0 and x is > 0, ±0 shall be returned.
If y is < 0 and x is ±0, −π/2 shall be returned.
If y is > 0 and x is ±0, π/2 shall be returned.
If x is 0, a pole error shall not occur.
If either x or y is NaN, a NaN shall be returned.
If the correct value would cause underflow, a range error may occur,
and atan(), atan2f(), and atan2l() shall return an implementation-
defined value no greater in magnitude than DBL_MIN, FLT_MIN, and
If the IEC 60559 Floating-Point option is supported, y/x should be
If y is ±0 and x is −0, ±π shall be returned.
If y is ±0 and x is +0, ±0 shall be returned.
For finite values of ±y > 0, if x is −Inf, ±π shall be returned.
For finite values of ±y > 0, if x is +Inf, ±0 shall be returned.
For finite values of x, if y is ±Inf, ±π/2 shall be returned.
If y is ±Inf and x is −Inf, ±3π/4 shall be returned.
If y is ±Inf and x is +Inf, ±π/4 shall be returned.
If both arguments are 0, a domain error shall not occur.
These functions may fail if:
Range Error The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO)
is non-zero, then errno shall be set to [ERANGE]. If the
integer expression (math_errhandling & MATH_ERREXCEPT) is
non-zero, then the underflow floating-point exception
shall be raised.
The following sections are informative.
Converting Cartesian to Polar Coordinates System
The function below uses atan2() to convert a 2d vector expressed in
cartesian coordinates (x,y) to the polar coordinates (rho,theta).
There are other ways to compute the angle theta, using asin() acos(),
or atan(). However, atan2() presents here two advantages:
* The angle's quadrant is automatically determined.
* The singular cases (0,y) are taken into account.
Finally, this example uses hypot() rather than sqrt() since it is
better for special cases; see hypot() for more information.
cartesian_to_polar(const double x, const double y,
double *rho, double *theta
*rho = hypot (x,y); /* better than sqrt(x*x+y*y) */
*theta = atan2 (y,x);
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The Open
Group Base Specifications Issue 7, Copyright (C) 2013 by the
Institute of Electrical and Electronics Engineers, Inc and The Open
Group. (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
applied.) In the event of any discrepancy between this version and
the original IEEE and The Open Group Standard, the original IEEE and
The Open Group Standard is the referee document. The original
Standard can be obtained online at http://www.unix.org/online.html .
Any typographical or formatting errors that appear in this page are
most likely to have been introduced during the conversion of the
source files to man page format. To report such errors, see
IEEE/The Open Group 2013 ATAN2(3P)