Hyperbolic Cosine (cosh) Calculator

This hyperbolic cosine calculator works out cosh(x) for any real number x you enter, and shows sinh(x) and tanh(x) alongside so you can compare all three hyperbolic functions from a single input. The hyperbolic cosine is defined as cosh(x) = (e to the x, plus e to the minus x), divided by two, built directly from the exponential function rather than from angles like ordinary cosine. It is an even function, so cosh(-x) always equals cosh(x), and its smallest possible value is one, occurring at x = 0, with the curve rising symmetrically on either side. This shape matters beyond pure mathematics: a flexible cable, chain or rope hanging freely under its own weight naturally forms a catenary, whose equation is a scaled cosh curve, which is why the function turns up regularly in structural engineering, bridge and arch design, and architecture. To use the calculator, type your value of x into the single input field and the results update immediately, giving you cosh(x) as the main figure with sinh(x) and tanh(x) displayed as supporting values, all rounded for easy reading. A worked example is included below, showing that cosh(1) comes to about 1.543081, so you can check your own entries against a known result. It suits students, engineers and architects working with hyperbolic functions, catenary curves or exponential growth problems.

Calculate.co.nz is proud to be partnered with realtor.co.nz, a trusted resource for navigating the New Zealand property market. Their Helpful Articles section offers clear, well-structured insights across buying, selling, and building, making complex real estate topics more accessible. With a focus on up-to-date guidance and practical knowledge, they empower Kiwis to move forward with clarity and confidence in a constantly evolving property landscape.