Built and fact-checked by the DocNectar team — see our editorial standards
Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
Mobile Friendly
Fully responsive design. Works on all devices & screen sizes.
Privacy Focused
Your data stays on your device. We don't store any inputs.
100% Free
No hidden costs. This tool is completely free forever.
The Kronecker product combines two matrices into a much larger one by scaling an entire copy of the second matrix by each element of the first — it shows up in signal processing, quantum computing, and constructing large structured matrices from smaller building blocks.
This calculator finds the Kronecker product of two matrices, each sized independently from 2×2 up to 6×6.
How it works
Enter the size and elements of Matrix A and Matrix B independently — they don't need to match in size. The calculator replaces each element of A with a scaled copy of the entire matrix B, arranging the resulting blocks in the same layout as A.
- Click Calculate to see your results.
Examples
A 2×2 example
For A = [[1,2],[3,4]] and B = [[0,5],[6,7]], the Kronecker product is a 4×4 matrix built from four scaled copies of B.
Who should use it
- Coursework involving tensor products or advanced linear algebra.
- Constructing large structured matrices from smaller components.
Industry applications
- Signal and image processing
- Quantum computing and physics
Advantages
- Handles matrices of different sizes for A and B.
- Shows the full block-by-block construction in the step-by-step solution.
Limitations
- The result grows quickly — a 6×6 combined with a 6×6 produces a 36×36 matrix.
Common mistakes to avoid
- Confusing the Kronecker product with standard matrix multiplication — they use completely different formulas and produce differently-sized results.
- Expecting the result to be the same size as the inputs — the Kronecker product always produces a larger matrix.
Best practices
- Double-check which matrix is A and which is B — although related, A⊗B and B⊗A are generally not the same matrix.
Tips
- Remember that A⊗B and B⊗A produce matrices of the same size and with the same entries overall, but arranged differently — they are not generally equal as matrices.