Dot Product Calculator
Enter two vectors with the same number of components.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- A · B = a₁b₁ + a₂b₂ + a₃b₃ + …
- Angle θ = arccos(A · B ÷ (|A| × |B|))
To get a vector instead of a number in 3D, use the cross product calculator.
Worked example
A = (1, 2, 3) and B = (4, 5, 6):
- A · B = 4 + 10 + 18 = 32
- Angle = 12.93°
Why your number may differ
The angle is only shown when neither vector is the zero vector. Results are rounded for display.
Frequently asked questions
What is the dot product?
Multiply the matching components of two vectors and add the results. The answer is a single number, not a vector.
What does a dot product of zero mean?
The two vectors are perpendicular (at 90°), provided neither is the zero vector.
How is the angle found?
cos θ = (A · B) ÷ (|A| × |B|), then take the inverse cosine.