Hyperbolic Cosine Calculator (cosh)
cosh(x) = (eˣ + e⁻ˣ) / 2. Catenary curve: y = a · cosh(x/a).
Result
cosh(x)
1.54308063
(e^1 + e^-1) / 2 = (2.7183 + 0.3679) / 2.
- x1
- eˣ2.71828183
- e⁻ˣ0.36787944
- cosh(x)1.5430806348
- sinh(x)1.1752011936
- tanh(x)0.7615941560
Step-by-step
- eˣ = 2.718282.
- e⁻ˣ = 0.367879.
- cosh(x) = (eˣ + e⁻ˣ) / 2 = 1.543081.
How to use this calculator
- Enter x.
- Read cosh(x) + companion sinh, tanh.
About this calculator
Hyperbolic cosine: cosh(x) = (eˣ + e⁻ˣ) / 2. Even function: cosh(−x) = cosh(x). Always ≥ 1 (minimum at x = 0). The catenary curve y = a·cosh(x/a) is the natural shape of a chain or cable hanging under gravity — and is famously different from a parabola, even though they look similar. Used in architecture (St. Louis Gateway Arch), suspension cable design.
Frequently asked
Both look like U shapes, but catenary y = cosh(x) has different curvature. The Gateway Arch is an inverted (weighted) catenary.
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