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ACOSH Function
Summary
The Excel ACOSH function calculates the inverse hyperbolic cosine of a number. This mathematical function returns the value whose hyperbolic cosine equals the input number, provided the input is 1 or greater. It's essential for advanced mathematical computations and engineering applications.
Syntax
ACOSH(number)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| number | Number |
Yes | Any real number equal to or greater than 1. Values less than 1 return a #NUM! error. |
Using the ACOSH Function
ACOSH is used in scientific calculations, engineering formulas, and statistical modeling where inverse hyperbolic functions are required. The function satisfies the relationship ACOSH(COSH(number)) = |number|, making it useful for reversing hyperbolic cosine operations.
Common ACOSH Examples
Basic ACOSH Calculation
=ACOSH(1)Returns 0, as the inverse hyperbolic cosine of 1 is 0.
Larger Value Example
=ACOSH(10)Returns approximately 2.9932228, the inverse hyperbolic cosine of 10.
Frequently Asked Questions
Common Errors and Solutions
#NUM!
Cause: Input number is less than 1
Solution: Ensure the number argument is ≥ 1
#VALUE!
Cause: Input is not a valid number
Solution: Provide a numeric value
Notes
- ACOSH(COSH(number)) equals the absolute value of number
- Always returns a non-negative result
- Useful in conjunction with other hyperbolic functions like COSH, SINH, TANH
Compatibility
Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365
Not available in: Excel 2003 and earlier
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+