How is the dot product calculated?

The dot product of a and b is aₓ·bₓ + aᵧ·bᵧ. It is zero when the vectors are perpendicular and equals |a||b|cos(θ).

Why is the 2D cross product a single number?

In two dimensions the cross product is the scalar aₓbᵧ − aᵧbₓ — the z-component of the 3D cross product. Its absolute value is the area of the parallelogram the two vectors span, and its sign gives their orientation.

Is anything uploaded?

No. All vector arithmetic runs locally in your browser.

2D Vector Calculator

Add, subtract, dot, cross and find the angle between 2D vectors.

2D vector operations in one place

Enter two planar vectors and this tool computes their sum and difference, the dot product, the scalar cross product, each vector’s magnitude, and the angle between them via the dot-product formula cos(θ) = (a·b) / (|a||b|).

The 2D cross product is reported as the signed scalar aₓbᵧ − aᵧbₓ. Everything is computed in your browser — no data leaves your device.