COSH
Returns the hyperbolic cosine of a number. Defined for all real numbers.
COSH(number)Arguments
numberAny real number for which to find the hyperbolic cosine.
=COSH(0)COSH(0) is always 1
=COSH(1)Hyperbolic cosine of 1
- •COSH(x) = (eˣ + e⁻ˣ) / 2
- •Result is always ≥ 1 for real inputs
- •Used in catenary curves (hanging cables, arches)
- •Confusing COSH with COS - COSH calculates the hyperbolic cosine, always returning a value of 1 or greater, while COS calculates the regular trigonometric cosine, which stays between -1 and 1
- •Expecting COSH's input to be an angle in radians the way COS's input is - COSH's argument is just a real number, with no geometric angle interpretation attached
- •Not recognizing that COSH grows extremely quickly for larger inputs, since it's built from exponential terms - values above roughly 700 will overflow Excel's maximum representable number
ACOSHPerforms the inverse operation - calculates the inverse hyperbolic cosine, undoing what COSH calculates, for inputs of 1 or greater.SINHCalculates the hyperbolic sine, a closely related function often used alongside COSH in the same formulas, like catenary curve calculations.COSCalculates the regular (non-hyperbolic) cosine, a different function despite the similar name, with a bounded output range of -1 to 1.What's the difference between COSH and COS?
They're unrelated despite the similar name - COSH is the hyperbolic cosine, always returning 1 or greater and taking any real number as input, while COS is the regular trigonometric cosine, bounded between -1 and 1 and interpreting its input as an angle in radians.
Why did COSH return a huge number?
COSH grows exponentially for larger inputs since it's derived from exponential terms - even moderately large numbers can produce enormous results, and inputs above roughly 700 will overflow Excel's number limits entirely.
What is COSH(0)?
Always 1 - this is a defining property of the hyperbolic cosine function, regardless of what other calculations surround it.
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