2×2 Matrix Determinant Calculator
Math
Find the determinant of a two-by-two matrix.
Formula
det(A) = a₁₁a₂₂ − a₁₂a₂₁
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
Example Calculation
Example inputs
- a₁₁: 1
- a₁₂: 2
- a₂₁: 3
- a₂₂: 4
The determinant of [[1,2],[3,4]] is −2.
Frequently asked questions
How do I use this calculator?
Enter a₁₁, a₁₂, a₂₁, a₂₂. The result updates automatically. Use Reset to restore the example values.
What method does it use?
det(A) = a₁₁a₂₂ − a₁₂a₂₁. Follow the units and definitions shown with the inputs to apply this relationship consistently.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.