---
title: "Cross Product Calculator — 3D Vectors, Perpendicular Vector & Area"
description: "Compute the cross product of two 3D vectors with step-by-step working. Finds the perpendicular vector, parallelogram area, triangle area, and angle. Uses the right-hand rule."
url: "https://worldcalculators.org/calculators/cross-product/"
canonical: "https://worldcalculators.org/calculators/cross-product/"
---

# Cross Product Calculator

Compute the cross product of two 3D vectors with step-by-step working. Finds the perpendicular vector, parallelogram area, triangle area, and angle. Uses the right-hand rule.

## Quick answer

Vector A (3D)

## Frequently Asked Questions

The dot product (A · B) produces a scalar and measures how parallel two vectors are. The cross product (A × B) produces a vector perpendicular to both and measures how perpendicular two vectors are. Both use the angle θ between vectors: dot uses cos(θ), cross uses sin(θ). Dot product works in any dimension; cross product only in 3D.
The cross product can be computed as a formal determinant: A × B = det([[î, ĵ, k̂], [ax, ay, az], [bx, by, bz]]), expanding along the first row. This is how it appears in most linear algebra textbooks (UK A-Level Further Maths, IB HL, US university curricula).

Source: https://worldcalculators.org/calculators/cross-product/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.