Cross Product Calculator
Free cross product calculator — step-by-step solution, worked examples, instant answers.
Cross product — determinant expansion, area and the right-hand rule.
About Cross Product Calculator
The Cross Product Calculator solves a × b = (a_yb_z − a_zb_y, a_zbₓ − aₓb_z, aₓb_y − a_ybₓ) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. The cross product exists only in 3D: it returns the perpendicular direction (right-hand rule: fingers a → b, thumb = a×b) with the spanned area as its length.
How to use Cross Product Calculator
- 1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
- 2The tool substitutes them into a × b = (a_yb_z − a_zb_y, a_zbₓ − aₓb_z, aₓb_y − a_ybₓ) and recomputes live.
- 3Read the answer in the result box, then expand the step-by-step solution to see the full working.
- 4Copy the method into your notebook, or change inputs to explore how the result behaves.
Why use Cross Product Calculator?
- ✓Solves a × b = (a_yb_z − a_zb_y, a_zbₓ − aₓb_z, aₓb_y − a_ybₓ) instantly as you type — no submit button, no waiting
- ✓Step-by-step solution shown for every calculation, not just the final answer
- ✓Realistic example values pre-loaded so you can see a worked example immediately
- ✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
- ✓Mobile-friendly and fast enough to use mid-homework or mid-lesson
Frequently asked questions
What formula does the Cross Product Calculator use?+
It uses a × b = (a_yb_z − a_zb_y, a_zbₓ − aₓb_z, aₓb_y − a_ybₓ). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.
What should I keep in mind when using this calculator?+
The cross product exists only in 3D: it returns the perpendicular direction (right-hand rule: fingers a → b, thumb = a×b) with the spanned area as its length. Torque, angular momentum and magnetic force are all cross products — and a × b = −(b × a), so order flips the sign.
Is the Cross Product Calculator free to use?+
Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.
Can I use this for homework, teaching or exam prep?+
That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.
Embed Cross Product Calculator on your website
Want Cross Product Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.
<iframe src="https://tooljolt.com/tools/cross-product-calculator" width="100%" height="640" style="border:1px solid #e5e7eb;border-radius:12px;max-width:680px" title="Cross Product Calculator — ToolJolt" loading="lazy"></iframe>Related Science tools
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