# Hyperbolic Functions Calculator

By Bogna Szyk
Last updated: Feb 07, 2018

Whether you are a high school student or a proficient mathematician, you will surely find this hyperbolic functions calculator useful. It is a tool that computes the values of six basic hyperbolic functions - sinh, cosh, tanh, coth, sech and csch - all in a blink of an eye. You can also use it to calculate the inverse hyperbolic functions.

## What are hyperbolic functions?

Hyperbolic functions are analogical to trigonometric functions that you probably know already, such as sine or cosine. What's the difference, then? If you plot points with coordinates (cos x, sin x) in a Cartesian coordinate system, they will form a circle. But if you plot points with coordinates (cosh x, sinh x), they will form a hyperbola. ## How to calculate sinh, cosh, and tanh?

All of these functions can be defined in terms of exponential functions. If you're not sure what these are, head to our exponent calculator for more detailed explanation.

If you want to calculate sinh(x) - the hyperbolic sine - you need to use the following formula:

`sinh(x) = (eˣ - e⁻ˣ) / 2`

The formula for calculating cosh(x) - the hyperbolic cosine - is quite similar:

`cosh(x) = (eˣ + e⁻ˣ) / 2`

You can calculate tanh(x), coth(x), sech(x) and csch(x) (hyperbolic tangent, cotangent, secant and cosecant) analogically as in trigonometry:

`tanh(x) = sinh(x) / cosh(x) = (eˣ - e⁻ˣ) / (eˣ + e⁻ˣ)`

`coth(x) = cosh(x) / sinh(x) = (eˣ + e⁻ˣ) / (eˣ - e⁻ˣ)`, x ≠ 0

`sech(x) = 1 / cosh(x) = 2/ (eˣ + e⁻ˣ)`

`csch(x) = 1 / sinh(x) = 2 / (eˣ - e⁻ˣ)`, x ≠ 0

## Inverse hyperbolic functions

Our hyperbolic functions calculator is also able to find the values of inverse hyperbolic functions. All you have to do is input the value of one of the functions (for example, sinh(x) or tanh(x)), and this tool will automatically return the value of x.

The formulas used to compute inverse hyperbolic functions are shown below.

`arsinh(x) = ln [x + √(x² + 1)]`

`arcosh(x) = ln [x + √(x² - 1)]`

`artanh(x) = 0.5 * ln [(1 + x) / (1 - x)]`

`arcoth(x) = 0.5 * ln [(x + 1) / (x - 1)]`

`arsech(x) = ln [(1 + √(1 - x²)) / x]`

`arcsch(x) = ln [1 / x + √(1 / x² + 1)]`

Bogna Szyk
x
sinh (x)
cosh (x)
tanh (x)
coth (x)
sech (x)
csch (x)
People also viewed…

### Millionaire

This millionaire calculator will help you determine how long it will take for you to reach a 7-figure saving or any financial goal you have. You can use this calculator even if you are just starting to save or even if you already have savings.

### Pizza size

This calculator will help you make the most delicious choice when ordering pizza.

### Polar coordinates

Polar coordinates calculator converts between Cartesian and polar coordinates in a 2D space.

### Triangular Prism

This triangular prism calculator determines the volume and surface area of that solid. 