Determinant Calculator
Compute the determinant of a 2x2, 3x3, or 4x4 matrix from a single grid.
Enter Values
Result
Enter values above and click Calculate to see your result.
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Formula
How it works: Select a size, enter entries, then evaluate the determinant with invertibility feedback.
Worked Example
What Determinants Tell You About a Matrix
The determinant is a single number that encodes fundamental properties of a square matrix. It tells you whether the matrix is invertible, how it scales volumes, and whether it preserves or reverses orientation.
- Nonzero determinant: the matrix is invertible, the system Ax = b has a unique solution, and the rows (or columns) are linearly independent
- Zero determinant: the matrix is singular, no inverse exists, and the system either has no solution or infinitely many
- Geometric meaning: the absolute value of the determinant equals the scaling factor for area (2D) or volume (3D) under the linear transformation
- Negative determinant: the transformation reverses orientation (like a mirror reflection)
This calculator computes determinants using cofactor expansion, the standard method taught in linear algebra courses.
You can also calculate changes using our Matrix Determinant Calculator, Determinant Calculator with Steps, 3x3 Determinant Calculator or 2x2 Determinant Calculator.
Frequently Asked Questions
How is this different from the other determinant calculators?
This is a single-page tool with a short URL optimized for the search term "determinant calculator." It uses the same cofactor expansion math as the dedicated 2x2, 3x3, and 4x4 calculators.
What if my matrix is singular?
The determinant equals zero, and the calculator reports that the matrix is not invertible. This means the rows are linearly dependent and the system has no unique solution.
Does a negative determinant mean an error?
No. Negative determinants are normal and mean the matrix reverses orientation (like reflecting across an axis). Only the sign and whether the value is zero or nonzero matter for most applications.
Which size should I select?
Choose 2x2 if you have 4 entries, 3x3 for 9 entries, or 4x4 for 16 entries. Extra fields are ignored for smaller matrix sizes.
Is it possible to embed the Determinant Calculator on another website?
Yes, embedding the Determinant Calculator is free. Hit the "Embed" button on this page, adjust the width, height, and theme, then grab the iframe code. It works on WordPress, Wix, Squarespace, Shopify, and plain HTML pages. No registration needed. Full instructions at calculory.com/services/embed-calculators.
AI Assistant
Ask about this calculator
I can help you understand the determinant calculator formula, interpret your results, and answer follow-up questions.
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