Everyday Tools

Determinant Calculator

Calculate the determinant of a 2x2 or 3x3 matrix.

Updated April 16, 2026
Free online tool
Planning and research use

Why this page exists

Small-matrix problems get easier when determinant formulas are handled directly instead of being expanded by hand every time. This calculator helps visitors calculate the determinant of a 2x2 or 3x3 matrix and clearly shows the matrix size and values used.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Determinant calculator

Calculate the determinant of a 2x2 or 3x3 matrix.

Result

-53

Calculated 3x3 determinant using the standard expansion formula.

Determinant value-53

Matrix size used3x3

Matrix values used[[2, 1, 3], [0, 4, -1], [5, 2, 1]]

Formula basis usedFirst-row expansion

Using the 3x3 matrix [[2, 1, 3], [0, 4, -1], [5, 2, 1]], the determinant comes to -53.
The 3x3 result is found by expanding across the first row and combining the signed 2x2 minors.
Use the result as a quick linear-algebra check for small matrices when you want the determinant without working through each step by hand.

This is standard matrix math for small matrices. The calculator supports 2x2 and 3x3 determinants only and expects one matrix entry in each field.

Planning note

Last updated April 16, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Choose whether you want to work with a 2x2 or 3x3 matrix.

Enter the matrix values in the matching grid.

The calculator applies the standard determinant formula for that matrix size and shows the result.

Understanding your result

This is standard determinant math for small matrices. The calculator supports 2x2 and 3x3 matrices only.

Browse more everyday tools

Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Check a homework or worksheet answer

A quick determinant result can make small-matrix problems easier to verify.

Compare determinant and trace

Looking at two matrix properties together can make the structure of a small matrix easier to discuss.

Use it with other algebra tools

Determinant questions often fit naturally beside formula, logarithm, and statistics tools.

FAQ

Common questions

What matrix sizes does this calculator support?

The calculator supports 2x2 and 3x3 matrices.

How is the 2x2 determinant calculated here?

The calculator multiplies the main diagonal entries and subtracts the product of the off-diagonal entries.

Why not support larger matrices?

This tool is designed as a quick small-matrix calculator rather than a full general-purpose linear-algebra solver.

Related tools

Keep comparing

Use these related tools to compare nearby scenarios, check a second estimate, or keep narrowing down the right decision.

Everyday ToolsUpdated April 16, 2026