Get The Angle Between Two Points

Angle Formula:

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

Point 1 X-coordinate (x₁):

Point 1 Y-coordinate (y₁):

Point 2 X-coordinate (x₂):

Point 2 Y-coordinate (y₂):

Angle Between Points (θ):

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1. What is the Angle Between Two Points?

Definition: This calculator determines the angle (in degrees) of the line connecting two points relative to the positive x-axis.

Purpose: It's useful in geometry, physics, engineering, and computer graphics for determining direction and orientation.

2. How Does the Calculator Work?

The calculator uses the arctangent function (atan2) with the formula:

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

Where:

\( \theta \) — Angle in degrees (0° to 360°)
\( (x_1, y_1) \) — Coordinates of the first point
\( (x_2, y_2) \) — Coordinates of the second point

Explanation: The function calculates the angle using the differences in y-coordinates and x-coordinates, handling all four quadrants correctly.

3. Importance of Angle Calculation

Details: Knowing the angle between points is essential for determining direction in navigation, analyzing slopes in engineering, and creating vector graphics.

4. Using the Calculator

Tips: Enter the coordinates of two points in meters (or any consistent unit). The angle is measured counterclockwise from the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system is used?
A: The calculator uses standard Cartesian coordinates with positive x to the right and positive y upwards.

Q2: How is the angle measured?
A: The angle is measured in degrees (0° to 360°) counterclockwise from the positive x-axis.

Q3: What if the points are the same?
A: The angle is undefined when both points are identical (division by zero).

Q4: Does this work for vertical lines?
A: Yes, the calculator handles vertical lines (90° or 270°) correctly.

Q5: Can I use different units?
A: Yes, as long as both x and y coordinates use the same units (meters, feet, etc.).