Calculate Angle Between Two Coordinates

Angle Calculation Formula:

\[ \theta = \operatorname{atan2}(y_2 - y_1, x_2 - x_1) \]

Point 1 X Coordinate:

Point 1 Y Coordinate:

Point 2 X Coordinate:

Point 2 Y Coordinate:

Angle (θ):

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1. What is the Angle Between Two Coordinates?

The angle between two coordinates represents the direction from point 1 to point 2 in a 2D coordinate system. It's calculated using the arctangent function (atan2) which considers the signs of both coordinates to determine the correct quadrant.

2. How Does the Calculator Work?

The calculator uses the atan2 function:

\[ \theta = \operatorname{atan2}(y_2 - y_1, x_2 - x_1) \]

Where:

\( (x_1, y_1) \) — Coordinates of the first point
\( (x_2, y_2) \) — Coordinates of the second point
\( \theta \) — Angle in radians (converted to degrees for display)

Explanation: The atan2 function calculates the angle between the positive x-axis and the vector from point 1 to point 2, returning a value between -π and π radians (-180° to 180°).

3. Importance of Angle Calculation

Details: Calculating angles between coordinates is essential in various fields including computer graphics, robotics, navigation, physics, and game development for determining directions and orientations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system does this calculator use?
A: This calculator uses the 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 is normalized to a range of 0° to 360°, measured counterclockwise from the positive x-axis.

Q3: How is atan2 different from regular atan?
A: atan2 takes both x and y differences as parameters and automatically determines the correct quadrant, unlike atan which only takes a single ratio and can't distinguish between angles in opposite quadrants.

Q4: Can this calculator handle negative coordinates?
A: Yes, the calculator works with any real number coordinates, both positive and negative.

Q5: What precision does this calculator provide?
A: The calculator provides results with 2 decimal places precision for the angle in degrees.