Programmers and Teachers:
What is a Determinant?
The determinant of a matrix is a number that can be calculated from a square matrix. It can be used for solving systems of linear equations and tells us about certain properties of the matrix, such as the volume scaling factor of the linear transformation described by the matrix.
The matrix determinant can also help tell us if the matrix has an inverse matrix or not. Also very importantly, the determinant helps us find the eigenvalues.
How to Calculate a Determinant by Hand
The method for calculating the determinant of a matrix depends on the size of the matrix. For a 1×1 matrix, the determinant is the number inside the matrix. For anything 2×2 and larger, we use shortcut methods that have a special order of multiplying, adding, and subtracting components.
For an in-depth explanation of how to hand calculate the determinant, see our determinant of a matrix lesson.
Example of a shortcut method for the determinant of a 3×3 matrix.
How the Calculator Works
The calculator on this page uses the same standard 2×2 matrix explicit method that a human uses. The image above shows this method applied to a 3×3 matrix.
Since the calculator can handle up to a 5×5 matrix, the software powering it actually breaks down large matrices into many 2×2 determinants that are solved sequentially. It is accurate to a minimum of the 5th decimal place!
Once the determinant from your inputted matrix is calculated, it is sent back here and displayed on the web page.