Dot Product Calculator
Scalar product and angle between vectors.
Reviewed by the Calculation Machine team · How we check our maths
Your values
ⓘ Live results
Results
- Dot product
- -15
- Angle between
- 122.073°
- |a|
- 6.16441
- |b|
- 4.58258
- Perpendicular?
- No
Quick answer
The dot product multiplies matching components and sums them, giving |a||b|cos θ.
The formula
a · b = Σ aᵢbᵢ = |a||b|cos θ
Worked example
Worked example
Using the values the calculator loads with.
Inputs
- Vector a3, -2, 5
- Vector b1, 4, -2
Result
- Dot product-15
- Angle between122.073°
- |a|6.16441
- |b|4.58258
- Perpendicular?No
How to use the Dot Product Calculator
- 1Enter the components of vector a.
- 2Enter the components of vector b.
- 3Both vectors must have the same length.
Frequently asked questions
What does a zero dot product mean?
The vectors are perpendicular.
Is the result a vector?
No, the dot product is a single number (a scalar).
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Report an error