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Eigenvalues of a 2×2 Matrix from Trace and Determinant Calculator

λ = (T ± √(T² − 4D)) / 2, T = a+d, D = ad−bc.

Compute the two eigenvalues of a real 2×2 matrix [[a,b],[c,d]] via the characteristic polynomial λ² − T·λ + D = 0, where T = trace = a+d and D = det = ad−bc. Reports T, D, the discriminant T² − 4D, both eigenvalues (only their real parts when complex), and a flag for real-vs-complex.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

λ = (T ± √(T² − 4D)) / 2.

In depth

Compute the two eigenvalues of a real 2×2 matrix [[a,b],[c,d]] via the characteristic polynomial λ² − T·λ + D = 0, where T = trace = a+d and D = det = ad−bc. Reports T, D, the discriminant T² − 4D, both eigenvalues (only their real parts when complex), and a flag for real-vs-complex.