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Instant Calculation
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Vectors combine magnitude and direction, and comparing two vectors — how aligned they are, how large each one is — comes down to a handful of standard operations.
This calculator finds the dot product, cross product, magnitude of each vector, and the angle between them, in 2D or 3D.
How it works
Choose 2D or 3D, then enter the components of each vector. The calculator applies the dot product formula to find alignment, the cross product formula to find a perpendicular result, and uses the dot product and magnitudes together to find the angle between the vectors.
- Enter dimension.
- Enter vector A — x.
- Enter vector A — y.
- Enter vector A — z (3D only).
- Enter vector B — x.
- Enter vector B — y.
- Enter vector B — z (3D only).
- Click Calculate to see your results.
Examples
A=(3,4), B=(1,2)
For 2D vectors A=(3,4) and B=(1,2), the dot product is 11, |A| is 5, |B| is about 2.24, and the angle between them is about 10.3°.
Who should use it
- Checking physics or linear algebra coursework involving vector operations.
- Computing the angle between two force or velocity vectors.
Industry applications
- Physics and engineering education
- Computer graphics and game development (vector math is foundational)
Advantages
- Handles both 2D and 3D vectors from a single tool.
- Reports dot product, cross product, magnitudes, and angle all in one calculation.
Limitations
- Doesn't support vector addition/subtraction or scalar multiplication directly.
Common mistakes to avoid
- Expecting a 3D-style cross product vector when working in 2D — the 2D case only has a single (z-component) value.
- Forgetting to select 3D and fill in the z-components when working with true 3D vectors.
Best practices
- Use the angle result to sanity-check your vectors — parallel vectors should show 0° or 180°, and perpendicular vectors should show exactly 90°.
Tips
- In 3D graphics and physics, the cross product is commonly used to find a vector perpendicular to two others — for example, to compute a surface normal from two edge vectors.