basic

Angle Between Vectors Calculator

Angle between two 3D vectors from the dot product.

Compute the angle between two 3D vectors using cos θ = (a·b) / (|a| · |b|), and report the angle in both degrees and radians.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

cos θ = (a·b) / (|a| · |b|)

In depth

Compute the angle between two 3D vectors using cos θ = (a·b) / (|a| · |b|), and report the angle in both degrees and radians.