The Excel ACOTH function returns the inverse hyperbolic cotangent of a number — the value whose hyperbolic cotangent (COTH) is the given number. The absolute value of the input must be greater than 1.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | A number whose absolute value is greater than 1 (i.e. number > 1 or number < -1). ACOTH returns the value whose COTH equals that number. |
How to use it
ACOTH is the inverse of COTH (the hyperbolic cotangent). Its result is a plain number, not an angle. The input's absolute value must exceed 1 — that is, number > 1 or number < -1:
Mathematically ACOTH(x) = 0.5 * LN((x + 1) / (x - 1)). Any input with |x| ≤ 1 (including values between -1 and 1, and exactly ±1) returns #NUM!. ACOTH was added in Excel 2013.
Domain is the opposite of ATANH: ATANH needs |x| < 1, while ACOTH needs |x| > 1. Values between −1 and 1 return #NUM! in ACOTH.
Try it: interactive demo
Pick a ACOTH example to see the formula and its result.
Practice workbook
Frequently asked questions
What versions of Excel have ACOTH?
=0.5*LN((number+1)/(number-1)).What input range does ACOTH accept?
number > 1 or number < -1). Anything with |x| ≤ 1 returns #NUM!.How does ACOTH's domain compare to ATANH's?
|x| < 1 while ACOTH requires |x| > 1.Is the ACOTH result an angle?
Master functions like this in one day
This page covers one function. Our Excel Formulas and Functions class covers the 30 that matter most — live, hands-on, taught by professionals in Dallas–Fort Worth, Houston, Austin, Oklahoma City, Denver, or online.
See the Formulas & Functions Class