Inverse Hyperbolic Tangent Calculator

The calculator will find the inverse hyperbolic tangent of the given value.

The inverse hyperbolic tangent $y=\tanh^{-1}(x)$ or $y=\operatorname{atanh}(x)$ or $y=\operatorname{arctanh}(x)$ is such a function that $\tanh(y)=x$.

It can be expressed in terms of elementary functions: $y=\tanh^{-1}(x)=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)$.

The domain of the inverse hyperbolic tangent is $(-1,1)$, the range is $(-\infty,\infty)$.

It is an odd function.

Related calculator: Hyperbolic Tangent Calculator