Determinant Calculator
Calculate determinant instantly in your browser.
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What this tool does
Calculate determinant instantly in your browser. Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
How to use the Determinant Calculator
- Enter or select matrix — rows separated by ; or new lines, entries by commas.
- Read the calculated result; change any measurement to compare alternatives.
Formula
The determinant is computed by cofactor expansion: for a 2×2 matrix [[a,b],[c,d]] it is ad − bc, and larger matrices expand into signed 2×2 minors along the first row. A determinant of zero means the matrix is singular (no inverse).
- matrix
- Matrix — rows separated by ; or new lines, entries by commas
Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
Worked example
For determinant calculator, the following measurements illustrate the exact method: Matrix — rows separated by ; or new lines, entries by commas: 1, 2, 3; 0, 4, 5; 1, 0, 6.
Inputs
- Matrix — rows separated by ; or new lines, entries by commas1, 2, 3; 0, 4, 5; 1, 0, 6
Result
- Determinant22
- Matrix size3 × 3
- Singular?No — an inverse exists
Results explained
- Determinant
- Determinant from the formula above. Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
- Matrix size
- Matrix size from the formula above. Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
- Singular?
- Singular? from the formula above. Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
Frequently asked questions
The determinant is computed by cofactor expansion: for a 2×2 matrix [[a,b],[c,d]] it is ad − bc, and larger matrices expand into signed 2×2 minors along the first row. A determinant of zero means the matrix is singular (no inverse).
Geometrically |det| is the area/volume scaling factor of the transformation the matrix represents.
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.