ACOS Function (OpenOffice Calc)
The ACOS function in OpenOffice Calc returns the arccosine (inverse cosine) of a value, in radians. Learn syntax, domain limits, examples, and best practices.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✔ |
| Libreoffice | ✔ |
| Numbers | ✔ |
| Onlyoffice | ✔ |
| Openoffice | ✔ |
| Wps | ✔ |
| Zoho | ✔ |
What the ACOS Function Does â–¾
- Returns the angle whose cosine equals the input
- Output is in radians
- Input must be between −1 and 1
- Useful for triangle geometry, dot products, and inverse trig calculations
- Works across sheets
ACOS is ideal when you need to recover an angle from adjacent/hypotenuse ratios or vector dot products.
Syntax â–¾
ACOS(number)
Arguments:
- number — A value between −1 and 1
ACOS returns an angle in radians.
Convert to degrees using:
Convert to degrees using:
ACOS(x) * 180 / PI()
Domain Rules â–¾
| Input | Valid? | Notes |
|---|---|---|
| −1 ≤ x ≤ 1 | ✔ | Required |
| x < −1 or x > 1 | ✘ | Undefined |
| text | ✘ | Error |
Mathematically:
[ \text{acos}(x) \text{ is defined only for } -1 \le x \le 1 ]
Basic Examples â–¾
Arccosine of 0.5
=ACOS(0.5)
Result (radians): 1.047197551
Convert arcsine to degrees
=ACOS(0.5) * 180 / PI()
Result: 60
ACOS using a cell reference
=ACOS(A1)
Convert degrees to radians before applying COS, then invert
=ACOS(COS(RADIANS(60)))
Advanced Examples â–¾
Recover angle from adjacent/hypotenuse ratio
=ACOS(Adjacent / Hypotenuse)
Angle between two vectors (dot product)
Given vectors (x1,y1,z1) and (x2,y2,z2):
=ACOS( (x1*x2 + y1*y2 + z1*z2) / (SQRT(x1^2+y1^2+z1^2) * SQRT(x2^2+y2^2+z2^2)) )
ACOS across sheets
=ACOS(Sheet1.A1)
ACOS in array formulas
=ACOS(A1:A10)
Confirm with Ctrl+Shift+Enter.
Recover angle from normalized vector
=ACOS(X / Length)
Solve for angle in a right triangle
=ACOS(Adj / Hyp)
Compute longitude from spherical coordinates
=ACOS(X / Radius)
Convert arcsine result to degrees
=DEGREES(ACOS(A1))
Common Errors and Fixes â–¾
ACOS returns Err:502 (Invalid argument)
Occurs when:
- Input < −1 or > 1
- Input is text
- Input is empty
- A malformed reference is used
ACOS returns unexpected results
Possible causes:
- Forgetting that output is in radians
- Using degrees without converting
- Ratios slightly outside range due to rounding
ACOS ignores values you expected it to include
ACOS ignores:
- Text numbers (
"123") - Empty cells
- Logical values
- Errors
ACOS includes values you expected it to ignore
ACOS includes:
- Dates
- Times
- Numeric results of formulas
Err:508 — Missing parenthesis
Usually caused by:
- Missing
) - Using commas instead of semicolons
Best Practices â–¾
- Always check that input is between −1 and 1
- Convert radians to degrees when needed
- Use ACOS for dot‑product angle calculations
- Use named ranges for triangle sides and vector components
- Pair ACOS with COS for reversible transformations
ACOS is the go‑to function for angles between vectors — especially when working with dot products or 3D geometry.