Det Calculator
Det calculator works out Determinant and Order (n) from Matrix, Method and Decimals shown. The default figures on this page give determinant of -306; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
8 steps
- Matrix is 3x3.
- [ 6 1 1 ]
- [ 4 -2 5 ]
- [ 2 8 7 ]
- Minor M(1,1) = -54, cofactor C(1,1) = -54.
- Minor M(1,2) = 18, cofactor C(1,2) = -18.
- Minor M(1,3) = 36, cofactor C(1,3) = 36.
- Expanding along row 1: det = (6)(-54) + (1)(-18) + (1)(36) = -306
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the det calculator calculates
Computes the determinant of a square matrix by cofactor expansion, row reduction or the Rule of Sarrus, and reports rank, trace and singularity.
How to use this det calculator
Enter Matrix, Method and Decimals shown. Determinant updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Determinant, Order (n) and Singular (det = 0).
The method follows Gilbert Strang, Introduction to Linear Algebra, ch. 5 (determinants) and Wikipedia, Determinant - Laplace expansion and Rule of Sarrus.
2x2 determinant example
With Matrix: 1 2; 3 4, the calculator returns Determinant: -2, Order (n): 2, Rank: 2. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Determinant, Order (n) and Singular (det = 0). The inputs you can vary are Matrix, Method and Decimals shown.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to find det on calculator?
Computes the determinant of a square matrix by cofactor expansion, row reduction or the Rule of Sarrus, and reports rank, trace and singularity. Open “How this is worked out” beside the result to see each step for your own figures.
How to calculate a det?
It needs Matrix, Method and Decimals shown. Nothing else is required, and the figures stay in your browser.
What is det a 1 equal to?
Computes the determinant of a square matrix by cofactor expansion, row reduction or the Rule of Sarrus, and reports rank, trace and singularity. On this page it is computed from Matrix, Method and Decimals shown and shown as Determinant, Order (n) and Singular (det = 0).
How to find the det of a 4x4 matrix?
The result gives Determinant, Order (n), Singular (det = 0), Invertible, Rank and Trace, each labelled with its unit so the figure can be read on its own.
What information do I need for the det calculator?
You need Matrix, Method and Decimals shown. The page opens with default figures that give determinant of -306, so you can see the scale before entering your own.
What does this det calculator show?
It shows Determinant, Order (n), Singular (det = 0), Invertible, Rank, Trace, Method used and Expansion, with the working and any warnings for your entries.