Quadratic Equation Calculator
Cubic Equation Calculator (real coefficients)
Quartic Equation Calculator
Quartic Equation Calculator (complex coefficients)

Cubic Equation Calculator
Complex Coefficients
To see the method of solving Cubic Equations, click here


Input MUST have the format:   AX3 + BX2 + CX + D = 0
Each coefficient may be real or complex. Examples of valid entries:
    3    -2.5    i    -i    2i    3+4i    3-4.5i    1+i7    2-i3    1e3+2e-2i

EXAMPLE: The cubic equation:   X3 - (3+i)X2 + (2+3i)X - 2i = 0
would be input:   A= 1   B= -3-i   C= 2+3i   D= -2i
Click E N T E R and your answers should be   1   2   and i

A= B= C= D=

X1=
X2=
X3=

I N S T R U C T I O N S

1) Do NOT enter commas.
2) Make sure that you have entered a number in ALL boxes (A, B, C and D).
3) If an equation has a 'missing' term (for example, no X2 term), enter it as zero. (Do NOT leave the field blank).
4) If an equation has a term with no coefficient, enter it as 1 (and not 0 or blank).
5) Write the imaginary unit as i, either after the number (2i, -3.5i) or before it (i2, -i3.5), or just i on its own. A complex number is the two parts joined with + or -: 3+4i or 3+i4.
6) Roots are polished with Newton's method after Cardano's formula, so very small real or imaginary parts (below 10-11) are shown as zero.

NOTE: This calculator uses the same method as the real-coefficient calculator, carried out entirely in complex arithmetic. With complex coefficients the sign of h no longer decides anything: S and U are always computed as complex cube roots, chosen so that S × U = -f/3, and the three roots are S + U, Sω + Uω2 and Sω2 + Uω (each minus b/3), where ω = -½ + (√3/2)i.
If you think it has calculated an incorrect answer, please send us an E-Mail.
And remember - you should always check your answers. Thank you.


To see the method for solving cubic equations, click HERE

If you want to use the "long hand" method for solving cubics, you may find the information in the boxes below very helpful to check your work as you go along. Here f, g and h are as on the method page, S and U are the two cube roots (S × U = -f/3), and X1 = S + U - b/3 where b = B/A.

f=
g=
h=
S=
U=

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