Cross Product Calculator
Compute the cross product A x B of two 3D vectors, returning the i, j, and k components of the resulting perpendicular vector.
What this calculator does
The Cross Product Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Compute the cross product A x B of two 3D vectors, returning the i, j, and k components of the resulting perpendicular vector. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Cross Product Calculator
This calculator finds the cross product of two three-dimensional vectors, A and B. You enter each vector as three comma-separated components (x, y, z), and it returns the i, j, and k components of A × B, the vector that is perpendicular to both inputs.
It is useful in physics and geometry for finding normal vectors, torque directions, or the area of a parallelogram spanned by two vectors. Each vector must include all three components.
Formula & Mathematical Calculation
i component = f(Vector A (x,y,z), Vector B (x,y,z))
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
For A = (1, 2, 3) and B = (4, 5, 6):
- i = (2×6 − 3×5) = 12 − 15 = −3
- j = (3×4 − 1×6) = 12 − 6 = 6
- k = (1×5 − 2×4) = 5 − 8 = −3
The calculator reports A × B = (−3, 6, −3).
Key Benefits
- Breaks the result into clear i, j, and k components
- Accepts each vector as a single comma-separated x,y,z entry
- Flags entries that do not contain three components per vector
How to Use this Calculator
-
Enter Vector A
Type the three components of the first vector into the 'Vector A (x,y,z)' field, separated by commas, such as 1,2,3. -
Enter Vector B
Type the three components of the second vector into the 'Vector B (x,y,z)' field, such as 4,5,6. -
Calculate
Press Calculate to see the i, j, and k components of the cross product.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Cross Product Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.