Three Dimensional Vector Angle Calculator

How to Use the Calculator

1. Enter the X, Y, and Z components of vector A in the respective input fields.
2. Enter the X, Y, and Z components of vector B in the respective input fields.
3. Click the "Calculate" button to compute the angle between the two vectors.
4. The result will be displayed in degrees.

Understanding the Formula

The angle θ between two vectors A and B is calculated using the dot product formula:

θ = arccos((A · B) / (||A|| × ||B||))

Where:
- A · B is the dot product of vectors A and B, calculated as A_x * B_x + A_y * B_y + A_z * B_z
- ||A|| is the magnitude (length) of vector A, calculated as √(A_x² + A_y² + A_z²)
- ||B|| is the magnitude (length) of vector B, calculated as √(B_x² + B_y² + B_z²)

Example

Suppose vector A = (1, 2, 3) and vector B = (4, 5, 6).

1. Calculate the dot product: A · B = 1*4 + 2*5 + 3*6 = 32

2. Calculate the magnitudes: ||A|| = √(1² + 2² + 3²) = √14, ||B|| = √(4² + 5² + 6²) = √77

3. Calculate the angle: θ = arccos(32 / (√14 * √77)) ≈ 22.02°