Angle Between Two Vectors Calculator
Vector Input
x
y
x
y
Results
Formulas Used
- Dot Product: a·b = |a||b|cos(θ)
- Angle: θ = arccos((a·b)/(|a||b|))
- Magnitude: |v| = √(x² + y² + z²)
Where:
a, b = vectors
θ = angle between vectors
Angle Between Vectors
-
degrees
Dot Product
-
scalar
Vector 1 Magnitude
-
units
Vector 2 Magnitude
-
units
About Vector Angles
The angle between two vectors is a fundamental concept in vector mathematics. Key points:
- The angle is always between 0° and 180°
- Perpendicular vectors have a 90° angle
- Parallel vectors have a 0° or 180° angle
- The dot product is maximum when vectors are parallel