Utilize our Angle Between Two Vectors Calculator to quickly determine the directional relationship between any two vectors in 2D or 3D space. This essential tool simplifies complex geometric calculations, providing accurate angles in degrees for your academic or professional needs.
Formula:
The angle θ between two vectors A and B is calculated using the dot product formula:
cos θ = (A · B) / (|A| |B|)
Therefore, θ = arccos((A · B) / (|A| |B|))
Where:
- A = Vector A (Ax, Ay, Az)
- B = Vector B (Bx, By, Bz)
- A · B = Dot product of A and B = (AxBx + AyBy + AzBz)
- |A| = Magnitude of Vector A = √(Ax2 + Ay2 + Az2)
- |B| = Magnitude of Vector B = √(Bx2 + By2 + Bz2)
If z-components are not provided, the calculation defaults to 2D.