When to use this calculator
Find a three-by-three matrix determinant by cofactor expansion. Enter rows in order. Floating-point cancellation can affect nearly singular matrices.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Two by Two Determinant Calculator: Find the determinant of a two-by-two matrix.
PUTTING IT INTO PRACTICE
Three by Three Determinant: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| a11 | 1 |
| a12 | 0 |
| a13 | 0 |
| a21 | 0 |
| a22 | 2 |
| a23 | 0 |
| a31 | 0 |
| a32 | 0 |
| a33 | 3 |
| Result | 6 |
- Check the input labels and enter the example values above.
- Apply the relationship: det = a(ei−fh) − b(di−fg) + c(dh−eg).
- The result is 6 , rounded for display.
How to interpret your result
Enter rows in order. Floating-point cancellation can affect nearly singular matrices.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the three by three determinant calculator useful?
Find a three-by-three matrix determinant by cofactor expansion. Enter rows in order. Floating-point cancellation can affect nearly singular matrices.
How do I use the three by three determinant calculator?
Enter a11, a12, a13, a21, a22, a23, a31, a32, a33. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
det = a(ei−fh) − b(di−fg) + c(dh−eg).
What should I check before using the result?
Enter rows in order. Floating-point cancellation can affect nearly singular matrices.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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