Documentation/Calc Functions/ATANH

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    Function name:

    ATANH

    Category:

    Mathematical

    Summary:

    Calculates the inverse hyperbolic tangent (artanh) of a real number, in radians.

    Syntax:

    ATANH(Number)

    Returns:

    Returns a real number that is the inverse hyperbolic tangent of Number in radians.

    Arguments:

    Number is a real number in the range (-1, 1), or a reference to a cell containing that number, whose inverse hyperbolic tangent is to be calculated.

    • If Number is non-numeric, then ATANH reports a #VALUE! error.
    • If Number lies outside the range (-1, 1), the ATANH reports an invalid argument error (Err:502).

    Additional details:

    The formula for the inverse hyperbolic tangent of x is:

    [math]\displaystyle{ \operatorname{artanh}(x) = \frac{1}{2}~ \ln\left (\dfrac{1+x}{1-x}\right ) }[/math]

    The figure below illustrates the function ATANH.

    ATANH function

    Examples:

    Formula Description Returns
    =ATANH(0) Inverse hyperbolic tangent of 0. 0
    =ATANH(TANH(4)) Inverse hyperbolic tangent of hyperbolic tangent of 4. 3.99999999999999
    =ATANH(D1) where cell D1 contains the number 0.5. Inverse hyperbolic tangent of 0.5. 0.549306144334055

    Related LibreOffice functions:

    ACOSH

    ACOTH

    ASINH

    FISHER

    TANH

    ODF standard:

    Section 6.16.11, Part 2

    Related (or similar) Excel functions:

    ATANH