1. What is the Angle Formula from Coordinates?

Definition: This calculator determines the angle (θ) between the positive x-axis and the line connecting the origin to point (x,y) in a 2D coordinate system.

Purpose: It's useful in mathematics, physics, engineering, and computer graphics for determining angles from coordinate data.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta \) — Angle in degrees
• \( y \) — Y-coordinate (vertical position)
• \( x \) — X-coordinate (horizontal position)

Explanation: The arctangent function (inverse tangent) calculates the angle whose tangent is the ratio of y to x.

3. Important Notes

Quadrant Awareness: The calculator returns values between -90° and 90°. For full 360° range, consider the signs of x and y:

• If x > 0 and y > 0: First quadrant (0°-90°)
• If x < 0 and y > 0: Second quadrant (90°-180°)
• If x < 0 and y < 0: Third quadrant (180°-270°)
• If x > 0 and y < 0: Fourth quadrant (270°-360°)

4. Using the Calculator

Tips: Enter the y and x coordinates in meters (or any consistent unit). The calculator handles all real numbers except x=0 (which would be undefined).

5. Frequently Asked Questions (FAQ)

Q1: What happens when x=0?
A: The calculation is undefined (vertical line). The angle is 90° if y>0 or -90° if y<0.

Q2: Does this work for 3D coordinates?
A: No, this is for 2D only. 3D angles require additional calculations.

Q3: How precise is the calculation?
A: The calculator provides results to 3 decimal places, sufficient for most applications.

Q4: Can I use negative coordinates?
A: Yes, the calculator handles negative values appropriately.

Q5: What's the difference between atan and atan2?
A: atan(y/x) gives -90° to 90°, while atan2(y,x) gives -180° to 180°, handling x=0 cases.