Vector Math
Dot Product Calculator
Calculate the dot product, individual magnitudes, and relative angle between any two vectors.
dot productscalar productangle
Dot Product
Compute the scalar product and angle between two vectors.
A · B
-9
‖A‖
3.741657
‖B‖
6.708204
Angle θ
1.93753 rad (111.0123°)
Dot product
A · B = Σ aᵢ bᵢ = ‖A‖ ‖B‖ cos θ
Along with the scalar result, the calculator reports the magnitudes and angle in both radians and degrees.
How to use
- Enter vector A and vector B using comma-separated components.
- Ensure both vectors share the same dimension.
- Review the dot product, magnitudes, and angle between the vectors.
Example
Input: A = (2, 1, −3), B = (4, −2, 5)
Output: A · B = −7, θ ≈ 110.6°
FAQ & notes
What if one vector is zero?
The dot product returns zero and the angle is undefined because it depends on both magnitudes.
Does the order matter?
No—the dot product is commutative, so swapping A and B produces the same result.