Cubic Equation Solver

About this calculator

This solver finds all roots of ax³ + bx² + cx + d = 0 using Cardano's method, the 16th-century algebraic technique that depresses the cubic (removing the x² term via substitution) and then solves the resulting form with a combination of cube roots. It reports the discriminant, whose sign tells you the nature of the roots before you even look at the numbers: positive means three distinct real roots, zero means a repeated real root, and negative means one real root plus a pair of complex conjugate roots.

Engineers and physicists hit cubics when solving for volumes, equilibrium points, or characteristic equations of certain systems, and math students use this to verify hand-worked Cardano's-method solutions, which are notoriously easy to make an arithmetic slip in given how many nested radicals are involved.