CALCULATE WITH CONFIDENCE

Algebra & Equations

Cubic Equation Calculator

Calculate cubic equation with validated inputs and explicit results.

Algebra & Equations

Enter values

Private calculation in your browser
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

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Understand the subject

What is Cubic Equation?

An equation states that two expressions have the same value. Solving means finding values that keep that balance true.

Use it to expose the allowed unknown value instead of changing one side without preserving equality.

The relationship

Write the rule before calculating

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

Enter the example values shown in the fields to verify the stated relationship.

Interpret with care

Important boundary

An algebraic step is valid only when it applies equally to both sides and does not divide by a possible zero quantity.

Use the Mathematics collection to move between connected concepts without duplicating the calculation.

Extended domain

All three cubic roots

A real cubic may have one real root and a complex-conjugate pair. This view reports all three rather than hiding the non-real solutions.

Try an example
COMPLEX RESULTr1 = 1r2 = -0.5 + 0.866025403784ir3 = -0.5 − 0.866025403784i

Principal branch

ReImr1r2r3

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

Solve ax³ + bx² + cx + d = 0 with the depressed-cubic method.

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

Enter the example values shown in the fields to verify the stated relationship.

Solve ax³ + bx² + cx + d = 0 with the depressed-cubic method.

Supported inputs

Precision and limits

Finite, bounded input

Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.

Notation

Enter ordinary finite decimals. Polynomial fields use coefficients in descending powers, separated by commas; for example 1, −3, 2 means x² − 3x + 2.