Dot Product Calculator
Compute the dot product, magnitudes, and angle between two vectors.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Dot Product Calculator
This tool computes the dot product (scalar product) of two vectors of any dimension.
- Enter Vector A. Type comma-separated values (e.g. 1, 2, 3).
- Enter Vector B. Must have the same number of components as A.
- View the result. The dot product, magnitudes, and angle update live.
About the Dot Product
The dot product of two vectors A and B is the sum of the products of their corresponding components: A . B = a1*b1 + a2*b2 + ... + an*bn. It is a scalar (single number), not a vector. The dot product relates to the angle between vectors through the formula A . B = |A| * |B| * cos(theta). When the dot product is zero, the vectors are perpendicular. The dot product is used extensively in physics, computer graphics, and machine learning.
Frequently Asked Questions
What does a dot product of zero mean?
A dot product of zero means the two vectors are perpendicular (orthogonal) to each other.
What is the difference between dot product and cross product?
The dot product returns a scalar and works in any dimension. The cross product returns a vector and is only defined for 3D vectors.
Do the vectors need to be the same length?
Yes. Both vectors must have the same number of components for the dot product to be defined.