Degree-three equation calculator
Cubic Equation Solver
Solve ax³ + bx² + cx + d = 0 and inspect all three real or complex roots with substitution residuals.
All entries and results stay in this browser tab. Nothing is uploaded, persisted, placed in the URL, or sent to analytics.
Enter known values
ax³ + bx² + cx + d = 0
Use ordinary decimal notation. Coefficient a must be nonzero.
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Roots
Classification:
Normalized equation:
Depressed-cubic discriminant:
Method
Coefficients are scaled, the monic cubic is reduced to a depressed cubic, and Cardano’s real cube-root branch or the trigonometric three-real-root branch is selected by a scale-aware discriminant tolerance. Every displayed root is independently substituted into the scaled polynomial.
Limitations
This is a cubic coefficient calculator, not a general expression parser or computer algebra system. Values must be finite ordinary decimals within the documented magnitude. When a is zero the page rejects the input and directs the user conceptually to the quadratic calculator.
Privacy
No account, server calculation, remote API, fetch, XHR, beacon, cookie, local storage, session storage, IndexedDB, or user-value telemetry is used.