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Math Calculators
Cubic Equation Calculator
Solve any cubic equation of the form ax³ + bx² + cx + d = 0 for its real roots.
Root 1
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Root 2
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Root 3
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About the Cubic Equation Calculator
A cubic equation ax³ + bx² + cx + d = 0 always has at least one real root. This calculator reduces it to a depressed cubic and solves it using Cardano's formula (one real root) or the trigonometric method (three real roots).
Formula: Substituting x = t − b/3a gives t³ + pt + q = 0, where p = c/a − b²/3a² and q involves a, b, c, d. The sign of q²/4 + p³/27 determines whether there is one real root or three.
Cubic equations appear in engineering, physics and volume-based optimization problems.
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