The Excel TANH Function

Hyperbolic Functions

The basic hyperbolic functions, cosh, sinh and tanh are related to the equilateral hyperbola, x2-y2=1.

If the area between a line through the origin, the x-axis, and the hyperbola x2-y2=1 has area α/2, then:

  • cosh α is the x coordinate of the intersection between the line through the origin and the hyperbola x2-y2=1
  • sinh α is the y coordinate of the intersection between the line through the origin and the hyperbola x2-y2=1
  • tanh α is equal to sinh α / cosh α
Hyperbolic Functions cosh and sinh

The equation used to calculate the hyperbolic tangent is therefore:

Hyperbolic Tangent Equation

Basic Description

The Excel Tanh function calculates the hyperbolic tangent (tanh) of a supplied number.

The syntax of the function is:

TANH( number )

Where the number argument is the real number that you want to calculate the hyperbolic tangent of.


Tanh Function Examples

The following spreadsheet below shows the Excel Tanh Function, used to calculate the hyperbolic tangent of three different values:

 Formulas:
Examples of use of the Excel Tanh Function
 Results:
Excel Tanh Function Results

For further details and examples of the Excel Tanh function, see the Microsoft Office website.


Tanh Function Error

If you get an error from the Excel Tanh Function, this is likely to be the #VALUE! error:

Common Error
#VALUE!-Occurs if the supplied number argument is not recognized as a numeric value.