Vector Calculator

What Is the Vector Calculator?

This calculator performs common vector operations — magnitude, dot product, angle between vectors, and cross product — for two 3D vectors. Leave the z-value at 0 for 2D vectors.

Formula

Magnitude: |V| = √(x² + y² + z²). Dot Product: A·B = AxBx + AyBy + AzBz. Angle: θ = cos⁻¹(A·B ÷ (|A||B|)). Cross Product: A×B = (AyBz−AzBy, AzBx−AxBz, AxBy−AyBx).

How to Use This Calculator

• Enter the x, y, and z components of Vector A (use 0 for z in 2D problems).
• Enter the x, y, and z components of Vector B.
• Click Calculate to see the magnitude, dot product, angle, and cross product.

Worked Example

For A = (3, 4, 0) and B = (4, 0, 0): |A| = 5, |B| = 4, A·B = 12, and the angle between them is about 36.87°.

Tips

A dot product of zero means the vectors are perpendicular. The cross product is only meaningful in 3D and always produces a vector perpendicular to both A and B.