The Excel COSH function returns the hyperbolic cosine of a number, defined as (e^x + e^−x) / 2. The argument is a plain number, not an angle in degrees.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | Any real number. COSH grows rapidly for large magnitudes, so very large inputs can overflow to a #NUM! error. |
How to use it
The hyperbolic cosine is built from the exponential function: COSH(x) = (EXP(x) + EXP(-x)) / 2. There is no degree-vs-radian issue — you pass a plain number:
COSH is an even function: COSH(-x) = COSH(x), and its smallest value is 1 at x = 0. Its inverse is ACOSH, and it pairs with SINH and TANH for the other hyperbolic ratios.
The catenary curve. A hanging chain or cable settles into the shape of a scaled COSH curve — which is why hyperbolic cosine appears throughout structural engineering and physics.
Try it: interactive demo
Pick a COSH example to see the formula and its result.
Practice workbook
Frequently asked questions
What is the hyperbolic cosine?
COSH(x) = (e^x + e^-x) / 2. Its minimum value is 1 (at x = 0) and it describes the shape of a hanging chain, called a catenary.Does COSH use degrees or radians?
Why is COSH never less than 1?
(e^x + e^-x)/2 is at least 1, reaching exactly 1 when x = 0. So COSH always returns a value of 1 or greater.What is the inverse of COSH?
ACOSH (inverse hyperbolic cosine) returns the number whose hyperbolic cosine is a given value; its argument must be 1 or greater.Master functions like this in one day
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