🎲Cubic Equation Solver
Find all three roots of ax³ + bx² + cx + d = 0 using Cardano's formula, with steps.
Free Cubic Equation Solver
Cubic equations don't factor as neatly as quadratics. Our free cubic equation solver finds all three roots of any ax³ + bx² + cx + d = 0, using Cardano's formula, with the full derivation shown — not just the final answer.
Enter your four coefficients and the calculator depresses the cubic, computes the discriminant, and applies Cardano's formula step by step. The discriminant tells you what to expect: three distinct real roots, a repeated real root, or one real root paired with two complex conjugate roots — each case labelled clearly, with complex roots shown in standard a ± bi form.
A graph of the cubic is plotted alongside the algebra, with real roots marked where the curve crosses the x-axis. No sign-up, no downloads, no limits.
About the Cubic Equation Solver
Features
Cardano's formula
The classical depression-and-substitution method shown step by step.
Discriminant classification
Automatically identifies three real roots, a repeated root, or a complex pair.
Complex root display
Complex roots shown in standard a ± bi form.
Graph
The cubic curve plotted with real roots marked at the x-axis crossings.
Frequently Asked Questions
How does the cubic equation solver work?
Enter the four coefficients of your cubic and it finds all three roots using Cardano's formula, with the full working shown.
Is it free?
Completely free, no sign-up, downloads, or limits.
Does it find complex roots?
Yes, when the discriminant is negative, one real root and a complex conjugate pair are shown in a ± bi form.
What is the discriminant used for?
It classifies the roots: three distinct real roots, a repeated real root, or one real root plus a complex pair.
What is Cardano's formula?
A classical method for solving cubic equations algebraically by first depressing the cubic to remove the squared term, then applying a formula involving the discriminant.
Does it show a graph?
Yes, the cubic curve is plotted with real roots marked where it crosses the x-axis.
Can it handle non-integer coefficients?
Yes, any real coefficients are accepted.
Are results exact or rounded?
Clean rational roots are shown exactly; irrational or complex roots are rounded to a sensible precision.
Is my data stored?
No; everything runs in your browser and isn't stored or sent.
Does it work on mobile?
Yes, fully responsive; the graph and steps adapt to smaller screens.