Matrix Multiplication Calculator
Math
Calculate matrix multiplication with explicit inputs and a worked example.
Formula
Cᵢⱼ = Σₖ AᵢₖBₖⱼ
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
Example Calculation
Example inputs
- Matrix A: 1, 2; 3, 4
- Matrix B: 5, 6; 7, 8
[[1,2],[3,4]] × [[5,6],[7,8]] gives [[19,22],[43,50]].
Frequently asked questions
How do I use this calculator?
Enter matrix a, matrix b. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Cᵢⱼ = Σₖ AᵢₖBₖⱼ. Follow the units and definitions shown with the inputs to apply this relationship consistently.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.