Vector Magnitude and Direction Calculator

Enter the x and y components of a 2D vector to instantly find its magnitude (length) and direction (angle).

X Component

Y Component

What this calculator finds

Every 2D vector can be described either by its components (how far it goes horizontally and vertically) or by its magnitude and direction (how long it is and which way it points). This calculator converts between the two.

The formulas

For a vector with components x and y, the magnitude (length) is found using the Pythagorean theorem: magnitude = √(x² + y²). The direction is the angle the vector makes with the positive x-axis, calculated as angle = atan2(y, x), converted to degrees and adjusted to fall between 0° and 360°.

This tool is for general math, physics, and engineering learning and planning purposes.

Last reviewed August 2026