Inverse Hyperbolic Tangent Function Calculator

Enter number：
Inverse hyperbolic tangent function：

What is an Inverse Hyperbolic Tangent Function Calculator?

An Inverse Hyperbolic Tangent (artanh or tanh⁻¹) Calculator computes the artanh(x) function, which returns the inverse hyperbolic tangent of a given number. The function solves for x in hyperbolic equations of the form:

The inverse function is:

Why Use an Inverse Hyperbolic Tangent Calculator?

  • Solves Hyperbolic Equations: Useful in physics, engineering, and signal processing.
  • Works in a Defined Range: Unlike arcsine or arccosine, artanh(x) is only valid for -1 < x < 1.
  • Scientific & Statistical Applications: Helps in probability theory, machine learning, and data normalization.

How Does It Work?

  1. Input: Enter a value x within the range (-1, 1).

  2. Processing: The calculator applies the formula:

  3. Output: Returns the corresponding artanh(x) value.

When Is It Used?

  • Physics & Engineering: Used in wave equations, relativity, and thermodynamics.
  • Machine Learning & Neural Networks: Activation functions like tanh are common in deep learning.
  • Finance & Economics: Applied in statistical models and risk analysis.
  • Signal Processing & Communications: Helps with data compression and transformations.