Math and Education
Cross Product Calculator
Cross Product Calculator calculate the three-dimensional vector cross product, magnitude, dot product, and angle between two vectors.
Math and Education
Cross Product Calculator
Calculate the three-dimensional vector cross product, magnitude, dot product, and angle between two vectors.
Formula
A x B = (AyBz-AzBy, AzBx-AxBz, AxBy-AyBx).
About the Cross Product Calculator
Calculate the three-dimensional vector cross product, magnitude, dot product, and angle between two vectors.
How the Cross Product Calculator Works
Cartesian components are combined with the determinant expansion, while dot product and magnitudes provide the angle and an orthogonality check.
Formula
A x B = (AyBz-AzBy, AzBx-AxBz, AxBy-AyBx).
The calculation runs in your browser. Values are validated for required ranges, compatible units, and method-specific restrictions before results are displayed.
Required Inputs
- Vector A x-component (required).
- Vector A y-component (required).
- Vector A z-component (required).
- Vector B x-component (required).
- Vector B y-component (required).
- Vector B z-component (required).
Results Reported
The result panel reports the final answer and the intermediate quantities needed to check the calculation:
- Cross-product vector
- Cross-product x-component
- Cross-product y-component
- Cross-product z-component
- Cross-product magnitude
- Dot product
- Angle between vectors (degrees)
Cross Product Calculator Example
Select Example Data in the calculator to load this reproducible input set:
| Input | Example value |
|---|---|
| Vector A x-component | 1 |
| Vector A y-component | 2 |
| Vector A z-component | 3 |
| Vector B x-component | 4 |
| Vector B y-component | 5 |
| Vector B z-component | 6 |
How to Use the Calculator
- Confirm that the calculator title and formula match the quantity you need.
- Enter every required value using the unit shown with its field.
- Select Example Data to inspect a valid input set, or enter your own values and select Calculate.
- Review all reported values and the displayed formula before using the answer.
- Use Copy Result or Download CSV when you need a reusable record.
Accuracy and Limitations
The cross product is defined here only for three-dimensional Cartesian vectors. A zero vector or parallel vectors do not define a unique angle normal.
Keep units consistent, use measurements that represent the actual situation, retain full precision during the calculation, and round only the final answer. Professional decisions may require current official rules, field measurements, laboratory methods, or specialist review.
Frequently Asked Questions
What does the Cross Product Calculator calculate?
Calculate the three-dimensional vector cross product, magnitude, dot product, and angle between two vectors.
Which formula does the Cross Product Calculator use?
A x B = (AyBz-AzBy, AzBx-AxBz, AxBy-AyBx). Cartesian components are combined with the determinant expansion, while dot product and magnitudes provide the angle and an orthogonality check.
What should I check before using the Cross Product Calculator result?
The cross product is defined here only for three-dimensional Cartesian vectors. A zero vector or parallel vectors do not define a unique angle normal.