Maths & numbers
3D vector calculator
Calculate lengths, dot and cross products, angle and vector projection.
A clear answer. Here’s how.
Uses Cartesian Euclidean vectors in three dimensions; set z=0 for a plane. Dot product is Σaᵢbᵢ, cross product uses right-handed coordinates, and angle = acos(dot/(|a||b|)). Projection of A onto B is B×dot(A,B)/|B|². Zero-vector unit directions, angles or projections are reported as undefined where needed. Components share one unit; products have its square.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Vector A · x
- 1
- Vector A · y
- 2
- Vector A · z
- 3
- Vector B · x
- 4
- Vector B · y
- 5
- Vector B · z
- 6
Example result
- Length of A
- 3.74165738677
- Length of B
- 8.77496438739
- Dot product A · B
- 32
- Cross product A × B
- (-3, 6, -3)
- Angle between A and B
- 12.9331544919 °
- Projection of A onto B
- (1.66233766234, 2.07792207792, 2.49350649351)
- Unit direction of A
- (0.267261241912, 0.534522483825, 0.801783725737)
- Unit direction of B
- (0.455842305839, 0.569802882298, 0.683763458758)