Hyperbolic tangent

Are you looking for a hyperbolic tangent calculator online? Below you will find one to get the result of this function for any real x-value.

Its operation is very simple. All you have to do is type the number x in the tanh calculator and click the calculate button to see the solution.

Hyperbolic tangent formula

Hyperbolic tangent formula

The hyperbolic tangent formula is defined as the quotient of the hyperbolic sine between the hyperbolic cosine of a real number x.

It is also possible to express this formula in exponential form.

Properties of the hyperbolic tangent

Graphic tanh

To better understand the properties of tanh(x) we wanted to show you its graphical representation. Thanks to this, we can clearly see that the hyperbolic tangent function of x has:

  • Domain: all real numbers, i.e., ranging from (-∞, +∞)
  • The range goes from (-1, +1)
  • Due to the previous point, we can intuit that the function has two horizontal asymptotes at y=-1 and at y=+1

Finally, it is a function bijective, odd, increasing and transcendental.

Hyperbolic tangent of PI

Now that we know much more about the hyperbolic tangent, we are going to see a particular case in which we will calculate the tanh(π)

tanh(π) = 0.996272076

The result we obtain is that for this value, the hyperbolic tangent is worth almost 1 if we do not need so much decimal precision. Remember that by its properties, the hyperbolic tangent will never reach a value of 1 although it approaches infinitesimally close to that value from certain quantities.

Derivative of hyperbolic tangent

The derivative of the hyperbolic tangent f(x) = tanhx is:

Derivative of the hyperbolic tangent

That is, it is the inverse of the hyperbolic cosine squared of x.

Integral of the hyperbolic tangent

If you want to know the integral of the hyperbolic tangenthere is the answer:

Hyperbolic tangent integral

As you can see, the integral of tanh(x) is equal to the natural logarithm of the hyperbolic cosine of x plus the constant C.

Identity of the hyperbolic tangent

There is an identity or formula that relates the hyperbolic tangent squared with the hyperbolic secant squared as follows:

tanh2x + sech2x = 1

This relation is especially useful for solving exercises in which we have to simplify or take out a common factor.

Calculate tanh in Excel

Hyperbolic Tangent Calculator

If in addition to using our tanh calculator online you want to make your own, you have the possibility to do it using Excel, Microsoft's spreadsheet program.

To do this, run the program, open a new spreadsheet and type in an empty cell the following function:


To get a result, you only have to write between the parentheses the value for which you want to calculate the hyperbolic trigonometric function. For example, if we want to calculate the hyperbolic tangent of 0, we will put it like this:


If the result returned by Excel is zero, then you have done it correctly.

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