2D Vector Calculator

Use this calculator to work with two vectors in the plane. Enter the components of A = (Ax, Ay) and B = (Bx, By). The results are the length of A, the dot product, the 2D cross product (a signed scalar), and the components of the vector sum A + B.

The formulas are: |A| = √(Ax² + Ay²), A·B = Ax Bx + Ay By, A×B = Ax By − Ay Bx, and A+B = (Ax + Bx, Ay + By). The dot product is positive when the vectors point in a similar direction, zero when they are perpendicular, and negative when they point opposite ways. In 2D the cross product is a scalar equal to twice the signed area of the parallelogram spanned by A and B; its sign follows the right-hand orientation of the plane.

Use the same component units for all four inputs. Magnitude and the sum components stay in those units; the dot product is in those units squared; the 2D cross product is also in those units squared.

A x: x-component of the first vector.

A y: y-component of the first vector.

B x: x-component of the second vector.

B y: y-component of the second vector.

|A|: Length of vector A.

A·B: Dot (scalar) product.

A×B (2D): Planar cross product, a signed scalar.

(A+B) x: x-component of the sum.

(A+B) y: y-component of the sum.