# Two Dimensional Vector Angle Calculation

Using this Online Calculator, we can Calculate the Angle for two vectors v & w

In 2D (Two Dimensional) vector there is only one degree of freedom for 2D rotations. If v and w are normalized

so that |v|=|w|=1, then angle = inverse of cosine (v X w)

where: |v|,|w| is magnitude of v,w.

In the case of two dimension vectors there is only one degree of freedom for rotations, and we can use the dot product to find the angle between 2 vectors.

If v and w are normalized so that |v|=|w| = 1

Therefore the angle θ between 2 vectors v and w can be find as

angle = arccos(|v||w|v•w)

where:

• • = dot- product

• arc cos = inverse of cosine function

• |v|= magnitude of vector v

Mostly acos returns a value between 0 and π which is 0° and 180°.