Calculate Angle With 2 Points

Angle Calculation Formula:

\[ \theta = \arctan2(y_2 - y_1, x_2 - x_1) \]

Point 1 X-coordinate:

Point 1 Y-coordinate:

Point 2 X-coordinate:

Point 2 Y-coordinate:

Calculated Angle:

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1. What is the Angle Calculation With 2 Points?

The angle calculation between two points uses the arctangent function (atan2) to determine the angle between the horizontal axis and the line connecting two points in a 2D coordinate system.

2. How Does the Calculator Work?

The calculator uses the atan2 formula:

\[ \theta = \arctan2(y_2 - y_1, x_2 - x_1) \]

Where:

\( x_1, y_1 \) — Coordinates of the first point
\( x_2, y_2 \) — Coordinates of the second point
\( \theta \) — The calculated angle in radians

Explanation: The atan2 function calculates the angle between the positive x-axis and the point (x2-x1, y2-y1), returning a value between -π and π radians, which is then converted to degrees.

3. Importance of Angle Calculation

Details: Calculating angles between points is fundamental in computer graphics, game development, robotics, navigation systems, and various engineering applications where direction and orientation are important.

4. Using the Calculator

Tips: Enter the coordinates of two points in a 2D plane. The calculator will determine the angle of the vector from point 1 to point 2 relative to the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system does this calculator use?
A: The calculator uses a standard Cartesian coordinate system with x increasing to the right and y increasing upward.

Q2: What is the range of the calculated angle?
A: The angle ranges from -180° to 180°, with 0° pointing to the right, 90° pointing up, -90° pointing down, and ±180° pointing left.

Q3: How is atan2 different from regular arctangent?
A: atan2 takes two arguments (y and x) and determines the correct quadrant for the angle, avoiding division by zero issues and providing more accurate results.

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

Q5: What applications use this type of angle calculation?
A: This calculation is used in computer graphics, game development, robotics path planning, navigation systems, and physics simulations.