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Angle Calculation Formula:
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The coordinate angle calculation determines the angle (in degrees) between the positive x-axis and the point (x,y) in a 2D Cartesian coordinate system. This is commonly used in mathematics, physics, engineering, and computer graphics.
The calculator uses the atan2 function:
Where:
Explanation: The atan2 function computes the angle in radians, which is then converted to degrees. Unlike the regular arctangent function, atan2 correctly handles all four quadrants.
Details: Calculating angles from coordinates is essential in many applications including vector mathematics, navigation systems, robotics, computer graphics, and game development. It helps determine direction and orientation in 2D space.
Tips: Enter both x and y coordinates. The calculator works with any real number values. The result will be an angle between 0° and 360°, measured counterclockwise from the positive x-axis.
Q1: What is the difference between atan and atan2?
A: atan2 takes both x and y coordinates as input and returns the correct angle in the appropriate quadrant, while atan only takes a ratio (y/x) and returns values only between -π/2 and π/2.
Q2: What does a negative angle mean?
A: Our calculator normalizes all results to 0-360 degrees. In the standard atan2 function, negative angles represent clockwise rotation from the positive x-axis.
Q3: What happens when both x and y are zero?
A: The angle is undefined at the origin (0,0) as there is no unique direction. Our calculator will not compute a result in this case.
Q4: How is this different from calculating slope?
A: Slope is the ratio y/x, while angle is the actual direction measured in degrees. Slope doesn't distinguish between opposite directions in different quadrants.
Q5: Can this be used for 3D coordinates?
A: No, this calculator is specifically for 2D coordinates. 3D angle calculations require additional parameters like azimuth and elevation angles.