How to Use the Angle Between Two Vectors Calculator

Enter the x, y, and z components of both vectors (use 0 for the z-component to work in 2D). The angle between them comes out in degrees.

θ = cos⁻¹((A · B) ÷ (|A| × |B|))

The dot product already encodes the angle between two vectors — it's largest when they point the same direction and negative when they point more than 90° apart — dividing by both magnitudes strips out the vectors' lengths and leaves a pure cosine value. Two perpendicular vectors always dot to zero no matter their length, which is the special case worth remembering: a dot product of zero means a 90° angle, full stop.