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ACOS Function (LibreOffice Calc)

Mathematical Beginner LibreOffice Calc LibreOffice 3.0

The ACOS function returns the arccosine (inverse cosine) of a number. The result is an angle expressed in radians, commonly used in trigonometry, geometry, and engineering calculations.

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

The **ACOS** function returns the **arccosine** (inverse cosine) of a number. The result is an angle in **radians**, ranging from 0 to π. It is widely used in trigonometry, geometry, physics, and engineering calculations.

What the ACOS Function Does

  • Computes the inverse cosine of a value
  • Returns an angle in radians
  • Accepts values in the range –1 to 1
  • Useful for triangle calculations, vector math, and geometric modeling

Syntax

ACOS(number)

Arguments

  • number:
    A numeric value between –1 and 1 inclusive.

Basic Examples

Arccosine of a value

=ACOS(0.5)
→ 1.047197551 (radians)

Convert result to degrees

=DEGREES(ACOS(0.5))
→ 60

Using a cell reference

=ACOS(A1)

Advanced Examples

Compute angle between two vectors

=ACOS( (A1*B1 + A2*B2) / (SQRT(A1^2 + A2^2) * SQRT(B1^2 + B2^2)) )

Compute angle in a triangle using the Law of Cosines

=DEGREES(ACOS((b^2 + c^2 - a^2) / (2*b*c)))

Normalize input to avoid domain errors

=ACOS(MAX(-1; MIN(1; A1)))

Combine with RADIANS for geometric modeling

=COS(RADIANS(ACOS(A1)))

Edge Cases and Behavior Details

ACOS returns a numeric value (radians)

Accepts:

  • Numbers between –1 and 1
  • Expressions that evaluate to numbers

Invalid input → Err:502

Behavior details

  • Input must be in the closed interval [–1, 1]
  • Output is in radians, not degrees
  • ACOS is undefined for values outside the domain
  • Use DEGREES() to convert the result

ACOS of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Input < –1 or > 1
  • Input is text

Fix:

  • Clamp values using MAX/MIN
  • Convert text to number with VALUE

Unexpected angle

Cause:

  • Forgetting that ACOS returns radians
  • Incorrect domain normalization

Fix:

  • Wrap with DEGREES
  • Validate input range

Best Practices

  • Always convert to degrees when working with human‑readable angles
  • Clamp floating‑point results to avoid domain errors
  • Use ACOS with vector dot products for geometric modeling
  • Combine with PI(), SIN(), COS(), and ATAN for full trigonometric workflows
ACOS is your inverse‑cosine workhorse — essential for geometry, physics, engineering, and any model involving angles or vector relationships.
  • Use COS for forward cosine
  • Use ASIN and ATAN for other inverse trig functions
  • Use DEGREES and RADIANS for angle conversion
  • Use PI() for circle and rotation calculations

By mastering ACOS and its companion functions, you can build precise, reliable trigonometric and geometric 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.

=ACOS(1)

Expected result: 0.

Find the angle in radians whose cosine equals 1.

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