Softonic

3D Vector Calculator

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Enter the x, y and z components of vectors A and B to calculate their magnitudes, sum, dot product, angle and the unit vector in the direction of A.

Operations and the zero-vector case

Magnitude is |A| = √(Ax²+Ay²+Az²), the sum is componentwise, and the dot product is A·B = AxBx+AyBy+AzBz. For two nonzero vectors, θ = arccos[(A·B)/(|A||B|)]. The unit vector is A/|A|.

An angle involving the zero vector is undefined because the formula would divide by zero. The zero vector also has no direction, so its unit vector is shown as unavailable instead of (0,0,0). This calculator handles real 3D Cartesian components only; it does not compute cross products or symbolic expressions. Inputs are sent to the site and may appear in the URL.

Frequently Asked Questions

The angle formula divides by both magnitudes, and the zero vector has magnitude zero and no direction.

Yes.

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