Vector Calculator
Enter the components (x, y, z) of two 3D vectors A and B — you get A+B, A-B, dot product, cross product, both magnitudes and the angle between them, all at once. For 2D, keep z = 0.
How to use
- Enter the x, y, z components of vector A.
- Enter the x, y, z components of vector B (z = 0 for 2D).
- All operation results appear in the result box.
Tips
- Working in 2D? Leave both z boxes at 0 and every formula still applies.
- A zero vector has no direction, so the angle with it is undefined — avoid all-zero inputs for the angle.
- Double-check the sign of each component: one flipped sign changes the sum, difference, products and angle.
Note: The dot product is a scalar: A.B = ax bx + ay by + az bz. The cross product is a new vector that is perpendicular to both. The angle comes from the dot product: cos theta = (A.B) / (|A| |B|).
Frequently Asked Questions (FAQ)
What vector operations are supported?
Addition, subtraction, dot product, cross product, both magnitudes and the angle between the two vectors.
Can I use 2D vectors?
Yes, enter the x and y components and keep z at 0 for 2D vectors.
What inputs does the vector calculator take?
The x, y and z components of two 3D vectors A and B. For 2D vectors, keep both z values at 0.
How is the angle between the vectors found?
From the dot product: the cosine of the angle equals the dot product divided by the two magnitudes multiplied.