In probability theory, the theorem of de Moivre-Laplace is a special case of the central limit theorem. It states that the binomial distribution of the number of "successes" in n independent Bernoulli trials with probability 1/2 of success on each trial is approximately a normal distribution if n is large, or, more precisely, that after standardizing, the probabilities converge to those assigned by the standard normal distribution.

The theorem first appeared in The Doctrine of Chances by Abraham de Moivre, published in 1733. The "Bernoulli trials" were not so-called in that book, but rather de Moivre wrote about the probability distribution of the number of times "heads" appears when a coin is tossed 1800 times.