Vector Math
Dot Product Calculator
Calculate the dot product, individual magnitudes, and relative angle between any two vectors.
Compute the scalar product and angle between two vectors.
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°
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Dot Product Calculator: vector calculator, vector addition calculator, dot product calculator, cross product calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Dot Product Calculator: Finds the scalar product plus the angle between vectors. It's built around dot product, scalar product, angle, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Along with the scalar result, the calculator reports the magnitudes and angle in both radians and degrees. The core relationship is A · B = Σ aᵢ bᵢ = ‖A‖ ‖B‖ cos θ, shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter vector A and vector B using comma-separated components. (2) Ensure both vectors share the same dimension. (3) Review the dot product, magnitudes, and angle between the vectors. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering A = (2, 1, −3), B = (4, −2, 5) returns A · B = −7, θ ≈ 110.6°. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
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.
What formula does the Dot Product Calculator use?
Along with the scalar result, the calculator reports the magnitudes and angle in both radians and degrees.
How do I use the Dot Product Calculator?
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.