ATAN2 Function (LibreOffice Calc)
The ATAN2 function returns the arctangent of the specified X and Y coordinates, producing an angle in radians with full quadrant awareness. It is essential for geometry, physics, engineering, and vector calculations.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✔ |
| Libreoffice | ✔ |
| Numbers | ✔ |
| Onlyoffice | ✔ |
| Openoffice | ✔ |
| Wps | ✔ |
| Zoho | ✔ |
What the ATAN2 Function Does ▾
- Computes the inverse tangent of Y and X
- Returns an angle in radians
- Correctly identifies the quadrant of the angle
- Handles all real numbers, including negative X and Y
- Avoids division-by-zero errors that occur with ATAN(Y/X)
Syntax ▾
ATAN2(number_y; number_x)
Arguments
-
number_y:
The Y coordinate (vertical component). -
number_x:
The X coordinate (horizontal component).
Basic Examples ▾
Angle of a vector (Y=1, X=1)
=ATAN2(1; 1)
→ 0.785398163 (π/4)
Convert to degrees
=DEGREES(ATAN2(1; 1))
→ 45
Angle pointing straight down
=DEGREES(ATAN2(-1; 0))
→ -90
Using cell references
=ATAN2(B1; A1)
Advanced Examples ▾
Compute angle of a 2D vector
=DEGREES(ATAN2(Y; X))
Compute direction between two points
=DEGREES(ATAN2(Y2 - Y1; X2 - X1))
Normalize angle to 0–360°
=MOD(DEGREES(ATAN2(Y; X)) + 360; 360)
Normalize angle to 0–2π
=MOD(ATAN2(Y; X) + 2*PI(); 2*PI())
Compute angle of a complex number
=ATAN2(IMAGINARY(A1); IMREAL(A1))
Use with vector dot/cross products
=DEGREES(ATAN2(A1*B2 - A2*B1; A1*B1 + A2*B2))
Edge Cases and Behavior Details ▾
ATAN2 returns a numeric value (radians)
Accepts:
- Any real numbers
- Zero values
- Negative values
Behavior details
- Output range: –π to π
- ATAN2(0; 0) returns 0
- ATAN2 handles quadrants correctly:
- (+X, +Y) → Q1
- (–X, +Y) → Q2
- (–X, –Y) → Q3
- (+X, –Y) → Q4
- ATAN(Y/X) cannot determine quadrant — ATAN2 solves this
Invalid input → Err:502 (non-numeric)
ATAN2 of an error → error propagates
Common Errors and Fixes ▾
Err:502 — Invalid argument
Cause:
- Text input
- Non-numeric values
Fix:
- Convert text to number with VALUE
- Validate numeric inputs
Unexpected angle
Cause:
- Forgetting ATAN2 returns radians
- Forgetting quadrant rules
- Using ATAN instead of ATAN2
Fix:
- Wrap with DEGREES
- Use ATAN2 for all X/Y angle calculations
Best Practices ▾
- Always use ATAN2 instead of ATAN(Y/X)
- Convert to degrees for human-readable angles
- Normalize angles when building navigation or rotation systems
- Use ATAN2 for vector, robotics, and physics calculations
- Use MOD to wrap angles into desired ranges
ATAN2 is the gold‑standard for angle calculations — accurate, quadrant‑aware, and essential for any vector‑based or directional model.
Related Patterns and Alternatives ▾
- Use ATAN for simple slopes when quadrant doesn’t matter
- Use DEGREES and RADIANS for angle conversion
- Use PI() for circular and rotational math
- Use IMARGUMENT for complex-number angles
By mastering ATAN2 and its companion functions, you can build precise, reliable geometric, physical, and engineering models in LibreOffice Calc.