Matrix Determinant Calculator
Choose the size and enter each row of the matrix.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- 2×2: det = ad − bc
- 3×3: det = a(ei − fh) − b(di − fg) + c(dh − eg), expanding along the first row
To find the inverse, use the matrix inverse calculator.
Worked example
The matrix with rows 2, 0, 1 / 1, 3, 2 / 1, 1, 4:
- det = 2 × (12 − 2) − 0 + 1 × (1 − 3) = 18
Why your number may differ
Values are rounded to 4 decimal places in the display. Larger matrices need a different tool.
Frequently asked questions
What is a determinant?
A single number from a square matrix that tells you, for example, whether the matrix can be inverted and how it scales area or volume.
How is a 2×2 determinant found?
For [[a, b], [c, d]] it is ad − bc.
What does a determinant of 0 mean?
The matrix is singular: it has no inverse, and its rows are dependent.