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Depressed Cubic (Cardano's Method) Real Root Calculator

Real root of x³ + px + q = 0 via Cardano's formula.

Finds the real cube root of the depressed cubic x³ + px + q = 0 using Cardano's formula: x = ∛(−q/2 + √D) + ∛(−q/2 − √D), where D = (q/2)² + (p/3)³.

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

D = (q/2)² + (p/3)³; x = ∛(−q/2+√D) + ∛(−q/2−√D)

In depth

Finds the real cube root of the depressed cubic x³ + px + q = 0 using Cardano's formula: x = ∛(−q/2 + √D) + ∛(−q/2 − √D), where D = (q/2)² + (p/3)³.