Dot Product Calculator
Scalar product and angle between vectors.
Enter your values
Enter the vector a you are working with.
Enter the vector b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
a · b = Σ aᵢbᵢ = |a||b|cos θ
At a glance
| What it does | Scalar product and angle between vectors. |
|---|---|
| Category | Math |
| Inputs needed | Vector a, Vector b |
| Main output | Dot product |
| Formula | a · b = Σ aᵢbᵢ = |a||b|cos θ |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Vector a
- Enter the vector a you are working with.
- Vector b
- Enter the vector b you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Vector a3, -2, 5
- Vector b1, 4, -2
Results
- Dot product-15
- Angle between122.073°
- |a|6.16441
- |b|4.58258
- Perpendicular?No
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).
What do I need to enter into the Dot Product Calculator?
Just 2 values: vector a, vector b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Dot Product Calculator work out the answer?
The dot product multiplies matching components and sums them, giving |a||b|cos θ. It applies the formula a · b = Σ aᵢbᵢ = |a||b|cos θ and shows the working so you can check each step by hand.
Is the Dot Product Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.