2x2 Determinant Calculator

Work out 2x2 determinant instantly with clear inputs, formula shown and shareable results.

About 2x2 Determinant Calculator

For a 2 × 2 matrix the determinant is ad − bc, the signed area of the parallelogram spanned by the rows. A zero determinant means the rows are parallel and the matrix collapses the plane onto a line.

Formula

2×2 determinant

det = ad − bc

Worked example

With the default values below, 2x2 Determinant Calculator returns Determinant ad − bc of -2.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Entry a (top left): 1
Entry b (top right): 2
Entry c (bottom left): 3
Entry d (bottom right): 4

Results

Determinant ad − bc: -2.00000000
Trace a + d: 5.00000000
Invertibility: Invertible
1/det, the inverse scaling factor: -0.50000000

Step by step

1Values used
22×2 determinant
3Determinant ad − bc= -2.00000000
4Trace a + d= 5.00000000
5Invertibility= Invertible
61/det, the inverse scaling factor= -0.50000000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Determinant of [[1,2],[3,4]]?

1 × 4 − 2 × 3 = −2.

What does a negative determinant mean?

The transformation reverses orientation — it flips the plane as well as scaling it.