3D Vector Calculator

Dot, cross, magnitude, and angle for 3D vectors

About this calculator

The 3D Vector Calculator computes the dot product, cross product, magnitudes, and the angle between two vectors in three dimensions. It also identifies whether the vectors are perpendicular, parallel, or anti-parallel, and shows an isometric diagram of both vectors and their cross product. Useful for physics, engineering, computer graphics, and linear algebra.

How to use the 3D Vector Calculator calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • a = (1, 2, 3), b = (4, 5, 6) → a · b = 32, a × b = (−3, 6, −3), angle ≈ 12.93°
  • a = (1, 0, 0), b = (0, 1, 0) → a · b = 0, angle = 90° (perpendicular)
  • a = (1, 2, 3), b = (2, 4, 6) → a × b = (0, 0, 0), angle = 0° (parallel)
  • a = (1, 2, 3), b = (−2, −4, −6) → angle = 180° (anti-parallel)
  • a = (2, 0, 0), b = (0, 0, 3) → a × b = (0, −6, 0), angle = 90°

Frequently asked questions

How does the 3D Vector Calculator calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the 3D Vector Calculator calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.