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ATAN Function (LibreOffice Calc)

Mathematical Beginner LibreOffice Calc LibreOffice 3.0

The ATAN function returns the arctangent (inverse tangent) of a number. The result is an angle expressed in radians and is widely used in trigonometry, geometry, physics, and engineering.

The **ATAN** function returns the **arctangent** (inverse tangent) of a number. The result is an angle in **radians**, ranging from –π/2 to π/2. It is widely used in trigonometry, geometry, physics, and engineering calculations.

What the ATAN Function Does

  • Computes the inverse tangent of a value
  • Returns an angle in radians
  • Accepts any real number
  • Useful for slope calculations, vector angles, and geometric modeling

Syntax

ATAN(number)

Arguments

  • number:
    Any real numeric value.

Basic Examples

Arctangent of a value

=ATAN(1)
→ 0.785398163 (π/4 radians)

Convert result to degrees

=DEGREES(ATAN(1))
→ 45

Using a cell reference

=ATAN(A1)

Advanced Examples

Compute angle of a slope (rise/run)

=DEGREES(ATAN(Rise / Run))

Angle between two vectors (tangent form)

=ATAN((A1*B2 - A2*B1) / (A1*B1 + A2*B2))

Normalize input for stability

=ATAN(VALUE(A1))

Compute arctangent using logarithmic identity (complex domain)

=IMDIV(IMSUB(IMLN(1 + IMSEC(A1)); IMLN(1 - IMSEC(A1))); 2*IMAGINARY(0))

Use ATAN with ATAN2 for full quadrant awareness

=ATAN2(Y; X)

Edge Cases and Behavior Details

ATAN returns a numeric value (radians)

Accepts:

  • Any real number
  • Expressions that evaluate to numbers

Behavior details

  • Domain is (–∞, ∞)
  • Output is in radians
  • ATAN(0) returns 0
  • ATAN does not determine the correct quadrant — use ATAN2 for that

Invalid input → Err:502 (non-numeric)

ATAN of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Input is text
  • Input cannot be coerced to a number

Fix:

  • Convert text to number with VALUE
  • Validate numeric input

Unexpected angle

Cause:

  • Forgetting ATAN returns radians
  • Using ATAN instead of ATAN2 for quadrant-sensitive calculations

Fix:

  • Wrap with DEGREES
  • Use ATAN2(X; Y) when direction matters

Best Practices

  • Convert to degrees for human‑readable angles
  • Use ATAN2 when both X and Y components are known
  • Combine with ACOS and ASIN for complete inverse‑trig workflows
  • Validate numeric input for stability
ATAN is your inverse‑tangent workhorse — essential for geometry, physics, engineering, and any model involving slopes or directional angles.
  • Use TAN for forward tangent
  • Use ATAN2 for full 2‑axis angle calculations
  • Use DEGREES and RADIANS for angle conversion
  • Use PI() for circle and rotation calculations

By mastering ATAN 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.

=ATAN(0)

Expected result: 0.

Calculate an angle from its tangent.

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