Dot Product Calculator
Instantly find the dot product of two vectors. This tool supports vectors up to 4 dimensions and shows the full calculation process.
What is the dot product of two vectors?
The dot product, also known as the scalar product, is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.
How do you calculate the dot product?
Multiply each corresponding component of the two vectors together and then sum those products. For 2D vectors: (a₁ × b₁) + (a₂ × b₂).
What does the dot product tell you?
The dot product measures how much two vectors are "pointing" in the same direction. If the dot product is positive, they point roughly the same way. If zero, they are perpendicular (orthogonal). If negative, they point roughly in opposite directions.
Is the dot product a vector or a scalar?
The dot product always results in a scalar (a single number), not a vector.