math

2D and 3D Vector Calculator

Calculate magnitude, unit vector, sum, difference, dot product, cross product, angle, and projection.

Calculator

Formula

a · b, a × b, proj_b(a)

Assumptions and limits

Inputs are finite real numbers unless an integer or probability is explicitly required.

Example

Editable worked example

The calculator starts with an editable example.

Sources

College Algebra 2e — OpenStax

Frequently asked questions

Are my inputs uploaded?

No. This calculator runs locally in your browser. Inputs are placed in a URL only when you explicitly copy a share link.

Why are units converted first?

Canonical units prevent scale errors when inputs use mixed units. The result is converted back to your selected output unit afterward.

Does the result replace professional judgment?

No. The result applies only to the stated model and assumptions. Qualified people should review high-risk engineering, medical, or laboratory decisions.