Calculator
What the Matrix Calculator does
Matrix Calculator: calculates A × B from A₁₁, A₁₂ and A₂₁. Example: A₁₁ 1, A₁₂ 2 and A₂₁ 3 gives a × b [[19, 22], [43, 50]].
A × B, derived from A₁₁, A₁₂, A₂₁ and A₂₂. You can nudge a single number and watch the effect straight away.
Most people who open the Matrix Calculator are students checking homework. A second opinion on a calculation takes seconds and prevents errors compounding.
There is no account, no upload and no server round trip, because the page does the work itself.
If you want to check the arithmetic, the field table, the method and a worked example are further down.
What do the Matrix Calculator fields mean?
The Matrix Calculator uses 8 inputs. You do not have to fill everything in before seeing an answer; the starting values already produce one.
| Field | What to enter | Default |
|---|---|---|
| A₁₁ | required | 1 |
| A₁₂ | required | 2 |
| A₂₁ | required | 3 |
| A₂₂ | required | 4 |
| B₁₁ | required | 5 |
| B₁₂ | required | 6 |
| B₂₁ | required | 7 |
| B₂₂ | required | 8 |
How does the Matrix Calculator work?
Each output is derived from the inputs above in a single pass; there is no hidden state carried between runs, so the same inputs always give the same calculation.
Checks happen up front, so errors surface next to the form instead of hiding in the output.
Worked example
These are the values the Matrix Calculator loads by default, and the result it produces from them. This is the worked example the page starts from, reproduced here so you can check the arithmetic.
| A₁₁ | 1 |
|---|---|
| A₁₂ | 2 |
| A₂₁ | 3 |
| A₂₂ | 4 |
| B₁₁ | 5 |
| B₁₂ | 6 |
| B₂₁ | 7 |
| B₂₂ | 8 |
| A × B | [[19, 22], [43, 50]] |
|---|---|
| What this means | 2×2 matrix product A×B |
How to use it
- Fill in A₁₁.
- Type A₁₂.
- Enter A₂₁.
- Set A₂₂.
- Put B₁₁.
- Key in B₁₂.
- Fill in B₂₁.
- Type B₂₂.
- Type a value and the answer is already there by the time you stop.
- The panel reports A × B and What this means.
- Copy Link puts the current inputs in the URL, so bookmarking it brings the same numbers back.
What this tool does not do
- Displayed values are rounded; the underlying calculation keeps full precision.
- Very large or very small values reach the limits of floating-point precision, about 15 significant digits.
- Defaults are illustrative starting points, not recommendations.
Frequently asked questions
8 things: A₁₁, A₁₂, A₂₁, A₂₂, B₁₁, B₁₂, B₂₁ and B₂₂. Every box already holds a working value, meaning you can explore the calculation before committing to real figures.
With the values loaded when the page opens, a × b comes out as [[19, 22], [43, 50]]. The figure is derived from the inputs above, so it updates whenever they do.
Nothing is logged. The tool is client-side code; your data stays where you entered it.
No. There is no account, no usage cap and no trial period. The site is funded by advertising rather than by charging for the tools.
It implements the published definition directly, without shortcuts or approximations.