ACOSH Function (LibreOffice Calc)
The ACOSH function returns the inverse hyperbolic cosine of a number. The result is expressed in radians and is used in advanced mathematics, engineering, and scientific modeling.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✔ |
| Libreoffice | ✔ |
| Numbers | ✔ |
| Onlyoffice | ✔ |
| Openoffice | ✔ |
| Wps | ✔ |
| Zoho | ✔ |
What the ACOSH Function Does ▾
- Computes the inverse hyperbolic cosine
- Returns an angle in radians
- Accepts values greater than or equal to 1
- Useful in scientific, engineering, and computational mathematics
Syntax ▾
ACOSH(number)
Arguments
- number:
A numeric value ≥ 1.
Basic Examples ▾
Inverse hyperbolic cosine of a value
=ACOSH(1)
→ 0
=ACOSH(5)
→ 2.292431669
Convert result to degrees
=DEGREES(ACOSH(5))
Using a cell reference
=ACOSH(A1)
Advanced Examples ▾
Compute ACOSH using its logarithmic identity
=LN(A1 + SQRT(A1^2 - 1))
Normalize input to avoid domain errors
=ACOSH(MAX(1; A1))
Hyperbolic triangle modeling
=ACOSH(COSH(A1) * COSH(A2) - SINH(A1) * SINH(A2) * COS(B1))
Engineering formula example
=ACOSH((V^2 + I^2 - R^2) / (2*V*I))
Edge Cases and Behavior Details ▾
ACOSH returns a numeric value (radians)
Accepts:
- Numbers ≥ 1
- Expressions that evaluate to numbers
Invalid input → Err:502
Behavior details
- Domain is [1, ∞)
- Output is in radians
- ACOSH is undefined for values < 1
- Use DEGREES() to convert the result
ACOSH of an error → error propagates
Common Errors and Fixes ▾
Err:502 — Invalid argument
Cause:
- Input < 1
- Input is text
Fix:
- Clamp values using MAX
- Convert text to number with VALUE
Unexpected result
Cause:
- Forgetting that ACOSH returns radians
- Using values close to 1 (results approach 0)
Fix:
- Wrap with DEGREES
- Validate input range
Best Practices ▾
- Always validate that input ≥ 1
- Convert to degrees when working with human‑readable angles
- Use ACOSH with COSH, SINH, and TANH for full hyperbolic modeling
- Combine with LN and EXP for scientific workflows
ACOSH is your inverse‑hyperbolic‑cosine tool — essential for engineering, physics, and advanced mathematical modeling.
Related Patterns and Alternatives ▾
- Use COSH for forward hyperbolic cosine
- Use ASINH and ATANH for other inverse hyperbolic functions
- Use LN and EXP for analytic transformations
- Use PI(), DEGREES, and RADIANS for angle conversions
By mastering ACOSH and its companion functions, you can build precise, reliable hyperbolic and scientific models in LibreOffice Calc.