The Excel ATANH function returns the inverse hyperbolic tangent of a number — the value whose hyperbolic tangent (TANH) is the given number. The input must be strictly between -1 and 1.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | A number strictly between -1 and 1 (exclusive). ATANH returns the value whose TANH equals that number. |
How to use it
ATANH is the inverse of TANH (the hyperbolic tangent). Its result is a plain number, not an angle. The input must be strictly between -1 and 1:
Mathematically ATANH(x) = 0.5 * LN((1 + x) / (1 - x)). The values -1 and 1 are excluded — the result heads to infinity at the edges — so =ATANH(1) or =ATANH(-1) returns #NUM!. ATANH is the Fisher z-transform used on correlation coefficients in statistics.
Open interval: ATANH needs an input greater than -1 and less than 1. Exactly ±1 (or beyond) returns #NUM! because the function is unbounded there.
Try it: interactive demo
Pick a ATANH example to see the formula and its result.
Practice workbook
Frequently asked questions
What input range does ATANH accept?
-1 and 1 (the endpoints are excluded). Exactly ±1 or beyond returns #NUM!.Why can't ATANH take exactly 1 or -1?
ATANH(x) heads to infinity as x approaches ±1, so those values are undefined and return #NUM!.Is the ATANH result an angle?
How is ATANH defined?
ATANH(x) = 0.5 * LN((1 + x) / (1 - x)), valid for −1 < x < 1.Master functions like this in one day
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