Vector Direction Calculator

Vector Direction and Unit Vector

The direction of a vector tells you which way it points. In 2D, the direction angle $\theta$ is measured counterclockwise from the positive x-axis. The unit vector $\hat{\mathbf{v}} = \mathbf{v}/|\mathbf{v}|$ has the same direction but length 1.

2D Direction Angle

For $\mathbf{v} = (x, y)$, use $\theta = \arctan(y/x)$ adjusted for the correct quadrant so $0° \leq \theta < 360°$.

Frequently Asked Questions

How do I find the direction of a vector?

In 2D, compute the angle from the positive x-axis using arctan(y/x) with quadrant correction. In 3D, use the unit vector or spherical angles.

What is a unit vector in the direction of v?

Divide each component by the magnitude: $\hat{\mathbf{v}} = \mathbf{v}/|\mathbf{v}|$.

Why does quadrant matter for direction angle?

arctan(y/x) alone only gives an angle relative to the nearest horizontal axis. Quadrant rules ensure the full 0° to 360° direction.

Can a zero vector have a direction?

No. The zero vector has magnitude 0, so division is undefined and direction is not defined.

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Vector Direction and Unit Vector

2D Direction Angle

Frequently Asked Questions

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