In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions.

For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides a so-called hyperbolic angle. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola xy = 1, or twice the area of the corresponding sector of the unit hyperbola x − y = 1, just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles.