What is the Direction of a Vector?
The direction of a two-dimensional vector is the angle it makes with the positive X-axis, measured counterclockwise. Given a vector with horizontal component x and vertical component y, this calculator returns that angle in degrees and radians, along with the vector's magnitude (length).
How to Use This Calculator
Enter the X component and the Y component of your vector. The tool computes the direction angle using the atan2 function, which correctly handles all four quadrants and returns a result normalized to the range 0° to 360°. The magnitude is also displayed so you have a full polar description of the vector.
The Formula Explained
The direction is calculated as
arctan(y/x), the two-argument atan2 uses the signs of both x and y to place the angle in the correct quadrant and avoids division by zero. The magnitude follows the Pythagorean theorem: Worked Example
For the vector (3, 4):
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