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Matrix Determinant Calculator

Compute the determinant of a 2x2, 3x3 or 4x4 matrix. Pick a size, fill the grid, done.

Matrix Determinant

Pick a size and fill the grid. Results update live.

Result
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Enter numbers to see the result.

Invertible?
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Method
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Formula: 2x2: ad - bc. 3x3: Sarrus rule. Larger: Gaussian elimination, det = (-1)^swaps x product of pivots.
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What the determinant means

The determinant is a single number that summarizes a matrix. A non-zero determinant means the matrix is invertible and its rows are independent; a zero determinant means it is singular, collapsing space flat. Geometrically it measures how the matrix scales area or volume.

How it is computed

For 2x2 the tool uses ad - bc and for 3x3 the Sarrus-style expansion. For 4x4 it uses Gaussian elimination with partial pivoting, tracking row swaps, then multiplies the pivots. All three give identical results on overlapping sizes.

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Matrix Determinant FAQs

What is the determinant of [[1,2],[3,4]]?
It is 1x4 - 2x3 = -2. Select 2 x 2 above; the default grid holds exactly this matrix.
What is the determinant of a singular matrix?
Zero. For example the default 4x4 grid has linearly dependent rows, so its determinant is 0 and the tool reports it as not invertible.
How do I know if a matrix is invertible?
Check the Invertible row: a non-zero determinant means the inverse exists. This is exactly the test the matrix inverse tool applies.
What is the determinant of the identity matrix?
Always 1, in any size. Enter 1s on the diagonal and 0s elsewhere to verify.
Is my matrix sent to a server?
No. The elimination runs entirely in your browser with JavaScript.
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