# Cross Product Calculator

Compute the 2D signed area or 3D cross product between two vectors

> Canonical page: https://elysiatools.com/en/tools/cross-product-calculator

- **Category:** Math & Numbers

- **Keywords:** cross product, vector product, signed area, 3d vector, math

## Overview

The Cross Product Calculator is a straightforward mathematical tool designed to compute the 3D cross product or 2D signed area between two vectors. By simply inputting the comma-separated coordinates of Vector A and Vector B, you can instantly find the perpendicular vector or determine the spatial relationship between them, with customizable decimal precision for accurate results.

## Inputs

- **Vector A** (text): e.g. 1, 2, 3
- **Vector B** (text): e.g. 4, 5, 6
- **Decimal Places** (number)

## When to use

- When you need to find a vector that is perpendicular to a given plane defined by two 3D vectors.
- When calculating the signed area of a parallelogram spanned by two 2D vectors.
- When verifying manual physics or linear algebra calculations involving torque, magnetic forces, or normal vectors.

## How it works

- Enter the comma-separated coordinates for Vector A (e.g., 1, 2, 3).
- Enter the comma-separated coordinates for Vector B (e.g., 4, 5, 6).
- Adjust the decimal places setting if you need a specific level of precision (from 0 to 10).
- The tool instantly calculates and outputs the resulting cross product vector or 2D signed area in JSON format.

## Use cases

- Calculating normal vectors for 3D graphics rendering and surface shading.
- Solving physics problems involving torque, angular momentum, or magnetic force.
- Determining the area and orientation of polygons in computational geometry.

## Frequently asked questions

### What formats are accepted for vector inputs?

Enter the vector components as comma-separated numbers, such as '1, 2, 3' for a 3D vector or '4, 5' for a 2D vector.

### Can I calculate the cross product of 2D vectors?

Yes. For 2D vectors, the tool computes the signed area (a scalar value) representing the magnitude of the cross product in the Z-direction.

### What happens if I input vectors of different dimensions?

Both vectors must have the same number of dimensions (either both 2D or both 3D) for the cross product to be mathematically defined.

### How do I control the precision of the result?

You can use the 'Decimal Places' setting to round the output values to your desired precision, up to 10 decimal places.

### Is the order of the vectors important?

Yes. The cross product is anticommutative, meaning Vector A × Vector B will yield a vector pointing in the exact opposite direction of Vector B × Vector A.

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