Angle Between Vectors Calculator

Published on: March 15, 2026
Final Answer: Free • Full Steps: Pro

This Angle Between Vectors Calculator helps you find the angle between two 3D vectors. First find the dot product of the vectors and the magnitude of each vector, then substitute those values into the angle formula. After simplifying, use the inverse cosine to get the final angle. It is a simple way to check answers, understand the method clearly, and practise vector operations step by step.

Step-by-step method

  1. Identify the vector components.
  2. Compute the dot product A · B.
  3. Compute the magnitudes |A| and |B|.
  4. Use θ = arccos((A · B) / (|A||B|)) and evaluate.

Formula:

\(\cos\left(\theta\right) = \frac{\vec{A} \cdot \vec{B}}{\left|\vec{A}\right|\left|\vec{B}\right|}\)