A cubic equation has an x³ term — the highest power is three.
About this calculator
A cubic equation has an x³ term — the highest power is three. Unlike quadratics, cubics always have at least one real root, and may have three. Enter coefficients a, b, c, d for ax³ + bx² + cx + d = 0.
The solver uses Cardano's method when one real root appears, and a trigonometric identity when three distinct real roots exist. Repeated roots show up when the discriminant is zero.
For degree-two problems use the [[quadratic]] calculator. For straight lines try the [[linear-equation]] calculator. For polynomial expansion practice see the [[foil-method]] calculator.
Common uses
- Find roots of cubic polynomials for calculus homework
- Check engineering curves that reduce to cubics
- Explore discriminant cases (one vs three real roots)
- Verify factorisation by comparing roots
Frequently asked questions
How many roots does a cubic have?
Up to three real roots (counting repeats). Complex roots come in conjugate pairs, so a cubic with real coefficients always has at least one real root.
What if a = 0?
The equation is not cubic — it drops to quadratic or linear. Enter a non-zero leading coefficient or use the quadratic calculator instead.
What is an example with three real roots?
x³ − 6x² + 11x − 6 = 0 factors as (x−1)(x−2)(x−3), roots 1, 2, and 3.
Does this show complex roots?
This tool lists real roots. When the discriminant is positive, only one real root is returned; the other two are complex conjugates.