Determinant Calculator
2×2 and 3×3 matrix determinants.
Enter your values
ⓘ Live results
Results
- Determinant
- 10
- Invertible?
- Yes
- Matrix size
- 2×2
- Area/volume scale factor
- 10
Quick answer
The determinant measures how a matrix scales area or volume; a determinant of zero means the matrix is singular.
det[[a,b],[c,d]] = ad − bc
How to use the Determinant Calculator
- 1Choose the matrix size.
- 2Enter values row by row, separated by commas.
- 3A zero determinant means no inverse exists.
Worked example
Using the values the calculator loads with:
Inputs
- Matrix size2×2
- Matrix values row by row4, 7, 2, 6
Results
- Determinant10
- Invertible?Yes
- Matrix size2×2
- Area/volume scale factor10
Frequently asked questions
What does a negative determinant mean?
The transformation flips orientation as well as scaling.
Why does zero matter?
The matrix collapses space to a lower dimension, so it cannot be inverted.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.