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ACOSH Function (LibreOffice Calc)

Mathematical Intermediate LibreOffice Calc LibreOffice 3.0

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.

Verification status: Consult the documentation and examples below. Native application testing has not been documented for this guide. How formula examples are checked

The **ACOSH** function returns the **inverse hyperbolic cosine** of a number. The result is an angle in **radians**, and the function is commonly used in engineering, physics, and advanced mathematical modeling.

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.
  • 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.

Reproducible example (tested in LibreOffice Calc)

This standalone example was calculated in LibreOffice Calc 25.2.3.2 and matched the expected value. It is a practical cross-check of one usage, not proof that every example elsewhere on this page is correct.

=ACOSH(1)

Expected result: 0.

Find the inverse hyperbolic cosine of 1.

If the result differs, check the referenced cells, argument separators and number formatting. For more information, consult the LibreOffice Calc official help.