# Documentation/Calc Functions/ATANH

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ATANH

Mathematical

## Summary:

Returns the inverse hyperbolic tangent of a number.

ATANH(Number)

## Returns:

This function returns the inverse hyperbolic tangent of Number, that is the value whose hyperbolic tangent is Number.

## Arguments:

Number is the real number, or a reference to a cell containing that number, which must be strictly between -1 and +1 whose inverse hyperbolic tangent value is to be calculated.

If the value of Number is outside this range, it returns an invalid error.

The formula for ATANH function is:

where N in the Number

The GIF 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. 4
=ATANH(0.5) Inverse hyperbolic tangent of 0.5. 0.549306144334055
=ATANH(1) Inverse hyperbolic tangent of 1 will return an invalid error because 1 is out of domain. Err:502

TANH

ACOTH

ACOSH

ASINH

ATAN

## ODF standard:

Section 6.16.11, Part 2

ATANH