Determinant Calculator
2×2 and 3×3 matrix determinants.
Enter your values
Choose one of: 2×2, 3×3.
Enter the matrix values row by row you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | 2×2 and 3×3 matrix determinants. |
|---|---|
| Category | Math |
| Inputs needed | Matrix size, Matrix values row by row |
| Main output | Determinant |
| Formula | det[[a,b],[c,d]] = ad − bc |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Matrix size
- Choose one of: 2×2, 3×3.
- Matrix values row by row
- Enter the matrix values row by row you are working with.
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.
What do I need to enter into the Determinant Calculator?
Just 2 values: matrix size, matrix values row by row. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Determinant Calculator work out the answer?
The determinant measures how a matrix scales area or volume; a determinant of zero means the matrix is singular. It applies the formula det[[a,b],[c,d]] = ad − bc and shows the working so you can check each step by hand.
Is the Determinant Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.