1. What is the atan2 Function?

The atan2 function is a two-argument variation of the arctangent function that computes the angle between the positive x-axis and the point (dx, dy). Unlike the standard arctan function, atan2 properly handles all four quadrants and avoids division by zero errors.

2. How Does the Calculator Work?

The calculator uses the atan2 formula:

Where:

• \( dy \) — Change in y-coordinate (vertical component)
• \( dx \) — Change in x-coordinate (horizontal component)
• \( \theta \) — Resulting angle in radians, converted to degrees

Explanation: The function returns the counterclockwise angle between the positive x-axis and the point (dx, dy), with proper quadrant determination.

3. Applications of Angle Calculation

Details: Angle calculation using coordinates is essential in computer graphics, robotics, navigation systems, physics simulations, and game development for determining direction and orientation.

4. Using the Calculator

Tips: Enter the change in y-coordinate (dy) and change in x-coordinate (dx). The calculator will compute the angle in degrees (0-360° range) measured counterclockwise from the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2 takes two arguments (dy, dx) and returns the correct quadrant, while atan takes one argument (dy/dx) and returns values only in the range -π/2 to π/2.

Q2: What angle range does atan2 produce?
A: The raw atan2 function returns values between -π and π radians (-180° to 180°). Our calculator normalizes this to 0-360° for convenience.

Q3: How does atan2 handle zero values?
A: atan2 properly handles cases where dx=0, returning ±90° or ±180° depending on the sign of dy, avoiding division by zero errors.

Q4: Can I use this for 3D coordinates?
A: This calculator is for 2D coordinates only. For 3D coordinates, you would need additional calculations involving spherical coordinates.

Q5: What are some practical applications?
A: Calculating angles between points, determining direction of movement, computer vision, aligning objects, and calculating rotation angles in various applications.