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A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula:
Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as an alias for the logistic function.
Special cases of the sigmoid function include the Gompertz curve and the ogee curve. Sigmoid functions have domain of all real numbers, with return value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value in the range 0 to 1. Another commonly used range is from −1 to 1.