Cross Product Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
| Component | Formula |
|---|---|
| i (x) | Ay·Bz − Az·By |
| j (y) | Az·Bx − Ax·Bz |
| k (z) | Ax·By − Ay·Bx |
| |A × B| | √(i² + j² + k²) |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
| Output | What it tells you |
|---|---|
| A × B vector | A new vector perpendicular to both A and B. |
| Magnitude | Equals the area of the parallelogram spanned by A and B. |
| Direction | Follows the right-hand rule from A to B. |
Formula & methodology
Formula: A × B = (Ay·Bz − Az·By, Az·Bx − Ax·Bz, Ax·By − Ay·Bx)
The cross product of two 3D vectors returns a third vector perpendicular to both, with length equal to the area of the parallelogram they span.
- Enter the x, y and z components of vector A.
- Enter the x, y and z components of vector B.
- The calculator applies the determinant formula for each component.
- Read the resulting vector and its magnitude.
Worked example: (2, 3, 4) × (5, 6, 7) = (3·7−4·6, 4·5−2·7, 2·6−3·5) = (−3, 6, −3).