Matrix Calculator
Add, subtract and multiply matrices, or calculate transpose, determinant and inverse for matrices up to 6 by 6.
- Add, subtract and multiply matrices
- Determinant, inverse and transpose modes
- Supports matrices up to 6 × 6 with row validation
Calculator workspace
Enter the known values, calculate, and review the supporting figures and formula instead of relying on a single unexplained number.
What this Matrix Calculator does
Matrices organize numbers into rows and columns and are used in linear algebra, computer graphics, statistics, optimization, engineering, economics and many data-processing workflows. This calculator handles the most common classroom and practical matrix operations in one workspace instead of forcing users to switch between separate tools. Matrices can be typed naturally with one row per line and values separated by spaces or commas.
The workspace is designed for quick checking as well as repeatable planning. Inputs remain editable, the supporting figures are shown with the headline result, and the calculation runs locally in the browser. That makes it easy to change one assumption at a time, compare scenarios and copy or save a result together with the values that explain it.
Formula and calculation method
Matrix multiplication uses Cᵢⱼ = Σ AᵢₖBₖⱼ. Determinant uses elimination; inverse uses Gauss–Jordan elimination.
For addition and subtraction, the calculator checks that A and B have exactly the same dimensions and then combines corresponding entries. Matrix multiplication checks that the number of columns in A equals the number of rows in B and builds every output entry from a row-by-column dot product. Transpose exchanges rows and columns. Determinant is evaluated with Gaussian elimination and row pivoting. Matrix inverse uses Gauss–Jordan elimination with partial pivoting and rejects singular matrices rather than returning an unstable or misleading result.
How to use the calculator
- Choose the calculation mode, shape, unit or known-value combination when the page provides one.
- Enter values that belong to the same problem or measurement scenario and keep units consistent with the field labels.
- Select Calculate and review both the main answer and the supporting metrics shown with it.
- Change one assumption at a time when comparing scenarios; this makes the effect of each input easier to understand.
- Use Copy Result, Share Result or Save Result Image when you need a portable record of the calculation.
Worked example
With A = [[1,2],[3,4]] and B = [[5,6],[7,8]], A + B is [[6,8],[10,12]], while A × B is [[19,22],[43,50]]. The determinant of A is −2, so A is non-singular and has an inverse. Choosing the inverse mode displays that inverse directly in the result area.
How to interpret the result
Always confirm dimensions before interpreting a matrix result. Addition and subtraction preserve the input dimensions, multiplication produces rows(A) × columns(B), and transpose reverses the dimensions. A determinant of zero means a square matrix is singular and has no inverse. Very small determinants can also signal numerical sensitivity, so high-stakes scientific work may require specialist numerical software with precision controls.
A calculator result is only as useful as the values entered. For measurements, use appropriately precise source data; for costs, use prices that match the same currency and period; for technical work, compare the output with drawings, equipment data or other authoritative information. The supporting metrics on this page are included specifically to make cross-checking easier.
Important assumptions and limitations
The browser calculator intentionally limits matrices to 6 × 6 to keep entry, validation and display manageable. It uses JavaScript floating-point arithmetic, so results containing repeating decimals or ill-conditioned matrices can show tiny rounding effects. The tool is intended for standard numeric matrices rather than symbolic algebra, exact fractions, complex-number matrices or sparse large-scale systems.
This calculator is provided for planning, checking, education and general informational use. It makes the formula and assumptions visible, but it does not replace project specifications, professional engineering, financial or medical advice, contractual documents, equipment ratings or applicable standards.
Frequently asked questions
How do I enter a matrix?
Put each row on a new line or separate rows with semicolons. Within a row, separate values with spaces or commas.
Why does matrix multiplication reject my matrices?
The number of columns in matrix A must equal the number of rows in matrix B.
Why does a matrix sometimes have no inverse?
A square matrix is invertible only when it is non-singular. A determinant of zero means no unique inverse exists.