Vector Calculator (Dot and Cross Product)
Perform vector operations — addition, dot product, magnitude and more.
Working with vectors
A vector has both magnitude and direction, unlike a plain number, and vectors have their own arithmetic used throughout physics, graphics and engineering. This performs the common vector operations, handling the component-by-component calculation for you.
Enter your vectors and choose an operation.
Why vectors need their own rules
Vectors represent things that have a direction as well as a size — a force, a velocity, a position — which is why they cannot be handled like ordinary numbers. Adding them combines their components, and geometrically it is placing them tip to tail, which is how you find the combined effect of two forces or motions. The dot product measures how much two vectors point the same way and is central to finding angles and projections, while the magnitude, found by the Pythagorean theorem across the components, gives the vector's length. These operations are the language of physics and 3D graphics, where everything from a spaceship's motion to a lighting calculation is vectors being added, scaled and combined by exactly these rules.
Common questions
How is a vector different from a number?
A vector has both magnitude and direction, so it represents things like force or velocity, and its arithmetic combines components rather than single values.
What does the dot product measure?
How much two vectors point in the same direction — central to finding angles between them and projecting one onto another.
Is anything uploaded?
No. The calculation happens in your browser.