Hyperbolic Sine (sinh) Calculator

This hyperbolic sine calculator works out sinh(x) for any real number x, along with the closely related cosh(x) and tanh(x), so you get all three hyperbolic functions from a single entry. Hyperbolic sine is defined from the exponential function as sinh(x) = (e^x - e^-x) / 2, and although its name echoes ordinary sine, the two behave quite differently: sinh is not periodic, it passes through zero at x = 0, it is an odd function so sinh(-x) = -sinh(x), and it grows without bound as x moves away from zero in either direction. Enter a value for x and the calculator instantly returns sinh(x) as the main result, with cosh(x) and tanh(x) shown alongside for comparison, all rounded for easy reading. Hyperbolic functions like this turn up widely in engineering and physics: they describe the curve of a hanging cable or chain, appear in solutions to heat flow and wave equations, and are standard tools in special relativity and electrical engineering. Students can use this page to check homework answers, engineers and physicists can use it to verify calculations quickly, and anyone curious about the maths can experiment with different values of x to see how the three functions relate to each other. A worked example below confirms sinh(1) is about 1.175201, so you can test the tool against a known value first.

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