2x2 Determinant Calculator

This 2 by 2 determinant calculator finds the determinant of a two by two matrix. Enter the four entries, reading across the top row then the bottom row, and the calculator returns the determinant, which is the top-left times bottom-right minus top-right times bottom-left. The determinant tells you a lot about the matrix: it is the scale factor for area under the matrix as a transformation, and the matrix can be inverted exactly when the determinant is not zero. It also appears in Cramer\u2019s rule and the cross product. The formula, a worked example and the assumptions are below.

a (row1)

b (row1)

c (row2)

d (row2)

Invertible?

Matrix

The formula

For the matrix with rows (a, b) and (c, d), the determinant is ad minus bc. The matrix is invertible exactly when this is non-zero, and the determinant equals the signed area of the parallelogram spanned by its rows.

Worked example

For the matrix with rows (1, 2) and (3, 4), the determinant is 1 times 4 minus 2 times 3 = 4 minus 6 = minus 2. Enter 1, 2, 3, 4 to confirm.

Frequently asked questions

How do I find a 2x2 determinant?

Multiply the main diagonal (top-left times bottom-right) and subtract the other diagonal (top-right times bottom-left): ad minus bc.

What does the determinant tell me?

Whether the matrix is invertible (non-zero) and how it scales area. Zero means the rows are parallel and the matrix is singular.

Where is it used?

In matrix inverses, Cramer\u2019s rule, area and the vector cross product.

Who this calculator is for

This calculator is for algebra students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard method is applied.
Results are rounded for display.

Formula and sources

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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