How to Use the Hyperbolic Function Calculator
Enter a single value of x to instantly calculate all six hyperbolic functions: sinh, cosh, tanh, coth, sech, and csch. Hyperbolic functions are built from the exponential functions e^x and e^-x: sinh(x) = (e^x - e^-x)/2, cosh(x) = (e^x + e^-x)/2, and tanh(x) = sinh(x)/cosh(x). The remaining three — coth, sech, and csch — are reciprocals of those three.
Hyperbolic functions appear throughout engineering and physics: the catenary curve of a hanging cable, velocity addition in special relativity, and the tanh activation function used in neural networks. This calculator also supports the inverse hyperbolic functions (asinh, acosh, atanh), so you can work backward from a value to find x.
Watch the domain restrictions, though. At x=0, sinh(0)=0, so coth and csch become undefined. Among the inverses, acosh only accepts inputs of 1 or greater, and atanh only accepts inputs strictly between -1 and 1. Outside those ranges, the calculator shows a clear error message.
Frequently Asked Questions
Since coth(x) = cosh(x)/sinh(x) and csch(x) = 1/sinh(x), both require sinh(x) in the denominator. At x = 0, sinh(0) = 0, so coth and csch are undefined at that point.
asinh is defined for all real numbers. acosh requires an input of 1 or greater. atanh is only defined for inputs strictly between -1 and 1.