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Cross Product Calculator

Online cross product: in 2D get the z-component; |z| is the parallelogram area.

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z=x₁y₂−y₁x₂
Vector a
x
y
Vector b
x
y

📖 Tutorial | Cross Product

1. Definition
In 2D the cross product is z=x₁y₂−y₁x₂=|a||b|sinθ, with |z| the parallelogram area; in 3D it is a vector.
2. Formula & Notation
zz-component
3. Properties & Laws
  • Anti-commutative;
  • Zero when collinear;
  • |z| is area;
  • In 3D a vector.
4. Steps
  1. Enter two vectors;
  2. Click "Cross";
  3. Or click "Load Example".
5. Worked Examples
Example: (1,2)×(3,4): z=−2.
6. Common Pitfalls
Order (anti-commute);
2D scalar, 3D vector;
Area uses absolute value.

❓ FAQ | Cross Product

2D?
z scalar.
Geometry?
Area.
3D?
Vector.
Anti-commute?
Yes.
Example?
z=−2.
Collinear?
0.