1. What is Angle Between Two Points?

Definition: This calculator determines the angle (θ) between two points in a 2D plane relative to the horizontal axis.

Purpose: It's useful in various fields including engineering, physics, computer graphics, and navigation to determine direction or orientation.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

Where:

• \( \theta \) — Angle in degrees
• \( (x_1, y_1) \) — Coordinates of first point
• \( (x_2, y_2) \) — Coordinates of second point

Explanation: The angle is calculated using the ratio of vertical change (Δy) to horizontal change (Δx) between the points.

3. Important Notes

Details:

• The angle is measured from the positive x-axis
• Result ranges from -90° to +90° (arctan range)
• For full 360° range, additional quadrant checks are needed
• When x₁ = x₂ (vertical line), the angle is 90° or -90°

4. Using the Calculator

Tips: Enter coordinates of two points in meters. The calculator will determine the angle between them relative to the horizontal axis.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system is used?
A: Standard Cartesian coordinate system with x increasing right and y increasing up.

Q2: How is the angle measured?
A: Angle is measured from the positive x-axis, positive counter-clockwise.

Q3: What if my points are the same?
A: The angle is undefined (calculator will show empty result).

Q4: Can I use different units besides meters?
A: Yes, as long as both points use the same units, the angle will be correct.

Q5: How accurate is the calculation?
A: Very accurate, using PHP's built-in trigonometric functions.