Determinant calculator
Type a square matrix, one row per line with the numbers separated by spaces, and get the determinant. Fractions such as 1/2 are allowed and the answer is exact.
One row per line, numbers separated by spaces. Fractions such as 1/2 are allowed.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How it is calculated
For a 2×2 matrix the determinant is ad − bc. Larger matrices are reduced to a triangular form with row operations (Gaussian elimination); the determinant is then the product of the pivots, with a minus sign for every row swap. That is much faster than expanding by cofactors and works up to 10×10.
What the determinant tells you
- det = 0: the rows are dependent, the matrix has no inverse and a system of equations with this matrix has no unique solution.
- det ≠ 0: the matrix is invertible. The absolute value is the factor by which the matrix scales areas (2×2) or volumes (3×3).
To find the inverse itself, use the inverse matrix calculator.
Frequently asked questions
Is the determinant calculator free?
Yes. The determinant calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.