3x3 Matrix Determinant Calculator
Determinant of a 3x3 matrix by cofactor expansion.
Enter your values
Enter the a you are working with.
Enter the b you are working with.
Enter the c you are working with.
Enter the d you are working with.
Enter the e you are working with.
Enter the f you are working with.
Enter the g you are working with.
Enter the h you are working with.
Enter the i 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
- -3
- Singular?
- No — matrix is invertible
Quick answer
The determinant is found by expanding along the first row with alternating signs and 2x2 sub-determinants.
det = a(ei-fh) - b(di-fg) + c(dh-eg)
At a glance
| What it does | Determinant of a 3x3 matrix by cofactor expansion. |
|---|---|
| Category | Math |
| Inputs needed | a, b, c, d, e, f, g, h, i |
| Main output | Determinant |
| Formula | det = a(ei-fh) - b(di-fg) + c(dh-eg) |
| Cost | Free — no sign-up, no download |
How to use the 3x3 Matrix Determinant Calculator
- 1Enter the nine entries of the matrix row by row.
- 2Cofactor expansion along the first row is applied automatically.
- 3A determinant of zero means the matrix has no inverse.
Inputs explained
- a
- Enter the a you are working with.
- b
- Enter the b you are working with.
- c
- Enter the c you are working with.
- d
- Enter the d you are working with.
- e
- Enter the e you are working with.
- f
- Enter the f you are working with.
- g
- Enter the g you are working with.
- h
- Enter the h you are working with.
- i
- Enter the i you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- a1
- b2
- c3
- d4
- e5
- f6
- g7
- h8
- i10
Results
- Determinant-3
- Singular?No — matrix is invertible
Frequently asked questions
What does a zero determinant mean?
The matrix is singular — its rows/columns are linearly dependent.
Can I use this for a 2x2 matrix?
Use the dedicated matrix determinant calculator for 2x2 matrices instead.
What do I need to enter into the 3x3 Matrix Determinant Calculator?
Just 9 values: a, b, c, d, e, f, g, h, i. 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 3x3 Matrix Determinant Calculator work out the answer?
The determinant is found by expanding along the first row with alternating signs and 2x2 sub-determinants. It applies the formula det = a(ei-fh) - b(di-fg) + c(dh-eg) and shows the working so you can check each step by hand.
Is the 3x3 Matrix 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.