Find The Angle Between Two Points

Angle Calculation Formula:

\[ \theta = \arctan\left(\frac{y_2 - y_1}{x_2 - x_1}\right) \]

x₁ (First Point X-coordinate):

y₁ (First Point Y-coordinate):

x₂ (Second Point X-coordinate):

y₂ (Second Point Y-coordinate):

Angle θ (degrees):

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1. What is the Angle Between Two Points?

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

Purpose: It's useful in geometry, physics, engineering, and computer graphics for determining directional relationships between points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \arctan\left(\frac{y_2 - y_1}{x_2 - x_1}\right) \]

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 arctangent of the slope between the two points, giving the angle relative to the positive x-axis.

3. Importance of Angle Calculation

Details: Knowing the angle between points is essential for determining direction, orientation, and relationships between objects in space.

4. Using the Calculator

Tips: Enter the coordinates of two points (x₁,y₁) and (x₂,y₂) in meters. The calculator will determine the angle between them.

5. Frequently Asked Questions (FAQ)

Q1: What range of angles does this produce?
A: The calculator returns angles between -90° and +90°. For full 360° range, additional quadrant checking is needed.

Q2: What happens when x₂ = x₁?
A: The line is vertical, so the angle is automatically set to 90° (straight up).

Q3: Does the order of points matter?
A: Yes, reversing the points will give you the opposite angle (θ vs θ+180°).

Q4: Can I use this for 3D points?
A: No, this is for 2D only. 3D angles require additional calculations.

Q5: How precise is the calculation?
A: The calculation is precise to 2 decimal places, sufficient for most applications.