Quadratic Formula Calculator

Easily solve quadratic equations with the Quadratic Formula Calculator from Math Tools. Get step-by-step solutions for accurate results. Try it now!

Enter coefficients

a (x²)

a must be a non-zero number.

Coefficient of x² (a ≠ 0).

b (x)

Enter a valid number.

c (constant)

Enter a valid number.

Decimal places

Choose 0–10 decimal places.

Graph x-min

Enter a valid number.

Graph x-max

Must be greater than x-min.

Graph samples

Enter an integer 25–500.

Results

Roots

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Ready

Enter a, b, c and click Calculate to solve ax² + bx + c = 0.

Detailed quadratic properties and forms.
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Graph of y = ax² + bx + c

Vertex and real x-intercepts (if any) are highlighted. Adjust x-range to zoom.

Tips

Discriminant (Δ): b² − 4ac. If Δ > 0, two real roots; Δ = 0, one real repeated root; Δ < 0, complex roots.
Vertex: x = −b/(2a), y = f(x). This is the maximum if a < 0, minimum if a > 0.
Vieta: Sum of roots = −b/a, product = c/a.

What is an Online Quadratic Formula Calculator?

An Online Quadratic Formula Calculator is a web-based tool that solves quadratic equations of the form $ax^2 + bx + c = 0$ using the quadratic formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

These calculators quickly compute the solutions (roots) of quadratic equations, whether real or complex, making them helpful for students, teachers, and professionals.

How to Use an Online Quadratic Formula Calculator?

Access the Calculator: Open a web browser and navigate to an online quadratic formula calculator website or app.
Input the Coefficients: Enter the values for $a$ , $b$ , and $c$ (the coefficients of the quadratic equation) into the designated fields.
Click Calculate: Press the "Calculate" or "Solve" button to compute the solutions.
View Results: The calculator will display the solutions, including real or complex roots. Some calculators may also show intermediate steps or the discriminant ( $b^2 - 4ac$ ).
Repeat or Adjust: Modify the coefficients to solve additional equations as needed.

Frequently Asked Questions-

Can the calculator handle equations with complex roots?
Yes, the calculator computes both real and complex roots and provides the solutions accordingly.
Does the calculator show the discriminant?
Many advanced calculators display the discriminant ( $b^2 - 4ac$ ) to help users understand whether the roots are real or complex.
Can I use it for equations where $a = 0$ ?
If $a = 0$ , the equation becomes linear ( $bx + c = 0$ ), and some calculators can handle this special case, but a quadratic formula calculator might prompt an error.
Are the results accurate?
Yes, online quadratic formula calculators are highly accurate as long as the input values for $a$ , $b$ , and $c$ are correct.
Do I need to simplify my equation before using the calculator?
No, you can input the coefficients directly as long as the equation is in the standard quadratic form $ax^2 + bx + c = 0$ .