The Excel ACOSH function returns the inverse hyperbolic cosine of a number — the non-negative value whose hyperbolic cosine (COSH) is the given number. The input must be 1 or greater.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | A number greater than or equal to 1. ACOSH returns the non-negative value whose COSH equals that number. |
How to use it
ACOSH is the inverse of COSH (the hyperbolic cosine). Its result is a plain number, not an angle. The input must be at least 1, because COSH never produces a value below 1:
Mathematically ACOSH(x) = LN(x + SQRT(x^2 - 1)). Feeding ACOSH a value below 1 returns #NUM!, since the square root would be of a negative number. The result is always non-negative.
Domain matters: ACOSH only accepts numbers ≥ 1. Values like 0 or 0.5 return #NUM! because COSH never dips below 1.
Try it: interactive demo
Pick a ACOSH example to see the formula and its result.
Practice workbook
Frequently asked questions
What input range does ACOSH accept?
≥ 1. A value below 1 returns #NUM!, because the hyperbolic cosine never goes below 1.Why does ACOSH(1) equal 0?
=ACOSH(1) returns 0.Is the ACOSH result an angle?
How is ACOSH defined?
ACOSH(x) = LN(x + SQRT(x^2 - 1)), valid for x ≥ 1.Master functions like this in one day
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