How to use the vector dot and cross product calculator
Compute dot product, cross product and angle for 3D vectors. Enter a x, a y, a z, b x, b y, b z in the fields above; the dot product, cross x, cross y, cross z, angle are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- ax — A x
- ay — A y
- az — A z
- bx — B x
- by — B y
- bz — B z
Worked example
With a x = 1, a y = 2, a z = 3, b x = 4, b y = -5, b z = 6, the calculator gives dot product ≈ 12; cross x ≈ 27; cross y ≈ 6; cross z ≈ -13; angle ≈ 68.56245 °.
Frequently asked questions
What is the formula for the vector dot and cross product calculation?
Dot product = ax × bx+ay × by+az × bz. Cross x = ay × bz-az × by. Cross y = az × bx-ax × bz. Cross z = ax × by-ay × bx. Angle (°) = acos([Dot product] / (hypot(ax,ay,az) × hypot(bx,by,bz))). Here ax is a x, ay is a y, az is a z, bx is b x, by is b y, bz is b z.
What inputs do I need for the vector dot and cross product calculator?
You need a x, a y, a z, b x, b y, b z. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.