The Standard Normal Cumulative Density Function

ASA066 is a C library which computes the cumulative density function of the standard normal distribution, by David Hill.

ASA066 is Applied Statistics Algorithm 66. Source code for many Applied Statistics Algorithms is available through STATLIB.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


ASA066 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA111, a C library which evaluates the percentage points of the normal distribution.

ASA241, a C library which evaluates the percentage points of the normal distribution.

NORMAL, a C library which samples the normal distribution.

PROB, a C library which evaluates and inverts a number of probabilistic distributions.

TEST_VALUES, a C library which contains sample values for a number of distributions.

UNIFORM, a C library which samples the uniform distribution.


Original FORTRAN77 version by David Hill; C version by John Burkardt.


  1. AG Adams,
    Algorithm 39: Areas Under the Normal Curve,
    Computer Journal,
    Volume 12, Number 2, May 1969, pages 197-198.
  2. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thacher, Christoph Witzgall,
    Computer Approximations,
    Wiley, 1968,
    LC: QA297.C64.
  3. David Hill,
    Algorithm AS 66: The Normal Integral,
    Applied Statistics,
    Volume 22, Number 3, 1973, pages 424-427.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C source codes.

Last revised on 01 November 2010.