In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one.
For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions.
A similar concept has been used in areas other than probability, such as for polynomials.