Determinant Calculator

Calculate matrix determinant. Free online determinant calculator for 2×2, 3×3, and larger matrices.

The Determinant Calculator finds the determinant of square matrices of any size. The determinant is a scalar value that encodes important properties of a matrix—whether it's invertible, how it scales area/volume, and more. Essential for solving systems of equations, finding inverses, and many linear algebra applications.

Common use cases

  • Checking matrix invertibility
  • Solving systems with Cramer's rule
  • Area/volume scaling factor
  • Eigenvalue calculations
  • Linear independence testing

How to use

  1. Select the matrix size (2×2, 3×3, etc.)
  2. Enter the matrix elements
  3. Click calculate for the determinant
  4. View the calculation method used
  5. Interpret the result

FAQ

What does determinant = 0 mean?

The matrix is singular (not invertible). Its rows/columns are linearly dependent.

How is 2×2 determinant calculated?

For [[a,b],[c,d]], det = ad - bc.

How is 3×3 determinant calculated?

Using cofactor expansion or the rule of Sarrus: a(ei-fh) - b(di-fg) + c(dh-eg) for standard form.

What does negative determinant mean?

The transformation reverses orientation (like a reflection). Magnitude still indicates scaling.