Hyperbolic Sine Calculator

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

About Hyperbolic Sine Calculator

The hyperbolic sine is sinh x = (eˣ − e⁻ˣ)/2, the odd part of the exponential. It parametrises the unit hyperbola in the same way sine parametrises the circle, and satisfies cosh²x − sinh²x = 1.

Formulas

Hyperbolic sine

sinh x = (eˣ − e⁻ˣ) / 2

Identity

cosh²x − sinh²x = 1

Worked example

With the default values below, Hyperbolic Sine Calculator returns sinh x of 1.17520119. Change any input above and every figure here is recalculated in your browser.

Inputs used

Value of x: 1
Multiply x by: 1

Results

sinh x: 1.17520119
cosh x: 1.54308063
tanh x: 0.76159416
eˣ: 2.71828183

Step by step

1Values used
2Hyperbolic sine
3Identity
4sinh x= 1.17520119
5cosh x= 1.54308063
6tanh x= 0.76159416
7eˣ= 2.71828183

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 8 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 sinh 1?

(e − 1/e)/2 ≈ 1.1752012.

Where does sinh appear physically?

In the catenary: a hanging chain follows y = a·cosh(x/a), and its arc length involves sinh.