Vector Calculator
Calculate vector addition, subtraction, dot product, cross product, or magnitude for 2D or 3D vectors.
Using this for 2D vectors
For 2D vector problems, simply leave both z fields at 0 — the calculator works the same way, just with the third dimension contributing nothing to the result, effectively reducing every operation to standard 2D vector math.
This is a common pattern in math and physics software — 2D problems are frequently treated as a special case of 3D with the third dimension held at zero, rather than needing entirely separate formulas.
Dot product vs. cross product
The dot product returns a single number (a scalar) and relates to the angle between two vectors — it's zero when vectors are perpendicular, and its sign tells you whether the vectors point in generally the same or opposite directions.
The cross product returns a new vector (only defined in 3D) that's perpendicular to both input vectors — it's used to find a normal vector to a plane, and its magnitude relates to the area of the parallelogram the two input vectors would form.
Frequently asked questions
Can I use this calculator for 2D vectors?
Yes — just leave both z fields at 0, and the math works the same way, since a 2D vector is simply a 3D vector with no third-dimension component.
Why is the cross product only defined in 3D?
The cross product's defining property — producing a vector perpendicular to both inputs — is a specifically 3-dimensional concept; in 2D there are infinitely many directions perpendicular to a plane's normal, so the same operation doesn't generalize the same way.