Math & Conversions

Quadratic Equation Calculator

Enter the coefficients a, b and c of ax^2 + bx + c = 0 and this calculator returns both roots, using the discriminant to report real or complex results. For a=1, b=-3, c=2 the roots are 2 and 1.

What this calculator does

The Quadratic Equation Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Enter the coefficients a, b and c of ax^2 + bx + c = 0 and this calculator returns both roots, using the discriminant to report real or complex results. For a=1, b=-3, c=2 the roots are 2 and 1. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Quadratic Equation Calculator

Result

—
Root 1
—
Root 2

About Quadratic Equation Calculator

The Quadratic Equation Calculator solves ax² + bx + c = 0. Enter the three coefficients and it computes the discriminant b² − 4ac, then returns two roots that are real when the discriminant is zero or positive and complex conjugates when it is negative.

Formula & Mathematical Calculation

Root 1 = f(a, b, c)

Calculated according to standard math formulas implemented in the calculator core.

Calculation Example

Enter a = 1, b = -3 and c = 2, then click Calculate. The discriminant is 1, so the tool shows Root 1: 2 and Root 2: 1 with the note 'Discriminant 1 (>=0): two real roots.'

Key Benefits

  • Solves any quadratic from its a, b and c coefficients
  • Reports the discriminant so you can see whether roots are real or complex
  • Returns complex conjugate roots in real + imaginary i form when the discriminant is negative
  • Blocks a = 0 with a clear message since that is not a quadratic

How to Use this Calculator

  1. Enter the coefficients
    Type values for a, b and c (a cannot be zero).
  2. Calculate
    Click Calculate.
  3. Read the roots
    Read the Root 1 and Root 2 boxes and the discriminant note below.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Quadratic Equation Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

The tool stops and shows 'Coefficient a cannot be zero for a quadratic,' because the equation would no longer be quadratic.

It returns complex conjugate roots written as real + imaginary i and real - imaginary i, and notes the discriminant is below zero.

Each root is rounded to four decimal places, dropping trailing zeros.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.