Inverse Hyperbolic Functions Calculator

An online calculator to calculate the inverse of hyperbolic functions is presented.

The six inverse hyperbolic functions are defined by [1]:

\( \text{arcsinh}(x) = \ln (x+\sqrt{x^2+1}) \quad , \quad (- \infty \lt x \lt \infty) \)
\( \text{arccosh}(x) = \ln (x+\sqrt{x^2-1}) \quad , \quad (x \ge 1) \)
\( \text{arctanh}(x) = \dfrac{1}{2} \ln \dfrac{1+x}{1-x} \quad , \quad (-1 \lt x \lt 1) \)
\( \text{arccoth}(x) = \dfrac{1}{2} \ln \dfrac{x+1}{x-1} \quad , \quad ( |x| \gt 1) \)
\( \text{arcsech}(x) = \ln \left( \dfrac{1}{x} + \sqrt{\dfrac{1}{x^2}-1} \right) \quad , \quad ( 0 \lt x \le 1) \)
\( \text{arccsch}(x) = \ln \left( \dfrac{1}{x} + \sqrt{\dfrac{1}{x^2}+1} \right) \quad , \quad (x \ne 0) \)

How to use the calculator

1 - Enter the variable \( x \) as a real number and the number of decimal places desired then press "Enter".