basic

Cross Product Magnitude and Direction from Two Vectors Calculator

|A×B| = |A||B|sin θ = a_x·b_y − a_y·b_x (2-D).

Calculates the cross product (scalar magnitude for 2-D vectors) and the angle between two 2-D vectors. The parallelogram area equals the magnitude of the cross product.

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

|A×B| = |ax·by − ay·bx|; Area = |A×B|; cos θ = A·B/(|A||B|)

In depth

Calculates the cross product (scalar magnitude for 2-D vectors) and the angle between two 2-D vectors. The parallelogram area equals the magnitude of the cross product.