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ATAN2 Function (LibreOffice Calc)

Mathematical Intermediate LibreOffice Calc LibreOffice 3.0

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.

The **ATAN2** function returns the **arctangent of Y/X**, but with **full quadrant awareness**, producing an angle in **radians** from –π to π. It is essential for vector math, navigation, robotics, physics, and geometry.

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.
  • 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.

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.

=ATAN2(1;0)

Expected result: 0.

Find the direction of the positive x-axis in radians; note coordinate order.

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