Key Facts
- Category
- Math, Date & Finance
- Input Types
- text, number
- Output Type
- json
- Sample Coverage
- 4
- API Ready
- Yes
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.
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
Examples
1. Finding a Normal Vector for 3D Graphics
3D Graphics Programmer- Background
- A developer is writing a custom shader and needs to find the normal vector of a triangle face to calculate lighting correctly.
- Problem
- Needs a vector perpendicular to two edge vectors of the triangle.
- How to Use
- Input the first edge vector '1, 2, 3' into Vector A and the second edge vector '4, 5, 6' into Vector B, keeping the default 6 decimal places.
- Example Config
-
Vector A: 1, 2, 3 | Vector B: 4, 5, 6 - Outcome
- The tool outputs [-3, 6, -3], which is the perpendicular normal vector used for the lighting calculation.
2. Calculating Polygon Area
Geometry Student- Background
- A student is verifying their homework on finding the area of a parallelogram defined by two 2D vectors.
- Problem
- Needs to quickly compute the 2D cross product (signed area) without manual arithmetic errors.
- How to Use
- Enter '3, 4' for Vector A and '1, 5' for Vector B.
- Example Config
-
Vector A: 3, 4 | Vector B: 1, 5 - Outcome
- The tool calculates the signed area, confirming the magnitude of the parallelogram's area is 11.
Try with Samples
math-&-numbersFAQ
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.