3D Vector Angle Calculator

Calculate the angle of three dimensional vectors (3D Vectors) with entered vector coordinates.

Calculator

Vector-1
Vector-2

 


Degrees

X Y Z θ Vector A Vector B Angle Formula cosθ = (A·B)/(|A||B|)

Formula

The angle between two 3D vectors is calculated using the dot product formula:

Where:

  • A · B = Dot product of vectors
  • |A| = Magnitude of vector A
  • |B| = Magnitude of vector B
  • θ = Angle between vectors

Example of 3D Vector Angle Calculation

Find the angle between vectors:

A = (2, 3, 4)

B = (5, 1, 7)

Dot Product:

(2×5) + (3×1) + (4×7) = 41

Magnitude of A:

√(2² + 3² + 4²) = √29

Magnitude of B:

√(5² + 1² + 7²) = √75

Angle:

θ = cos⁻¹(41 / (√29 × √75))

θ ≈ 28.44°

Frequently Asked Questions

How do you find the angle between vectors?

The angle between vectors is calculated using the inverse cosine of the dot product divided by the product of vector magnitudes.

Can the angle between vectors be 90 degrees?

Yes. If the dot product equals zero, the vectors are perpendicular.

What is the range of vector angles?

The angle between vectors ranges from 0° to 180°.