Hyperbolic Cosine Calculator

Work out hyperbolic cosine instantly with clear inputs, formula shown and shareable results.

About Hyperbolic Cosine Calculator

The hyperbolic cosine is cosh x = (eˣ + e⁻ˣ)/2, the even part of the exponential. It is never less than 1, and the curve y = a·cosh(x/a) is the catenary traced by a freely hanging chain.

Formulas

Hyperbolic cosine

cosh x = (eˣ + e⁻ˣ) / 2

Catenary

y = a·cosh(x / a)

Worked example

With the default values below, Hyperbolic Cosine Calculator returns cosh x of 1.54308063. Change any input above and every figure here is recalculated in your browser.

Inputs used

Value of x: 1
Catenary parameter aminimum 0: 1

Results

cosh x: 1.54308063
sinh x: 1.17520119
cosh²x − sinh²x (should be 1): 1.0000000000
a·cosh(x/a): 1.54308063

Step by step

1Values used
2Hyperbolic cosine
3Catenary
4cosh x= 1.54308063
5sinh x= 1.17520119
6cosh²x − sinh²x (should be 1)= 1.0000000000
7a·cosh(x/a)= 1.54308063

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is cosh 1?

(e + 1/e)/2 ≈ 1.5430806.

Is a catenary the same as a parabola?

No, though they look similar near the bottom. A hanging chain is a catenary; a parabola arises when the load is uniform per horizontal distance, as in a suspension bridge deck.