Quadratic Formula Calculator – Solve Equations Online
Solve ax² + bx + c = 0 with the quadratic formula, real or complex roots.
About the Quadratic Formula Calculator
What is the Quadratic Formula Calculator?
A quadratic formula calculator solves any quadratic equation ax² + bx + c = 0 and reports real or complex roots.
Why use this calculator?
Quadratics appear in physics (projectiles), finance, geometry and optimization, so a reliable solver is a maths workhorse.
How to use it
- Enter the coefficients a, b and c.
- Read the discriminant, the vertex and the roots.
- Complex roots are shown in a ± bi form when needed.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a.
The discriminant b² − 4ac decides real, repeated or complex roots.
Frequently Asked Questions
What does the discriminant tell us?
Greater than zero: two real roots. Zero: one repeated root. Negative: no real roots (two complex ones).
Can a quadratic have infinite roots?
Only if all coefficients are zero, which stops being a quadratic. A true quadratic has at most two roots.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.
How accurate are the results?
We use standard, widely accepted formulas and calculate in your browser using double-precision arithmetic. Results are rounded for readability, so treat them as reliable estimates rather than a guarantee. Real-world factors can vary the true figure.
Can I add this calculator to my own website?
Yes. Open this calculator page and use the "Add to your website" box in the sidebar to copy a ready-made iframe snippet, then paste it into any HTML page.
Does it work on a phone or tablet?
Yes. The layout is fully responsive, so it works on desktops, laptops, tablets and mobile phones, and every input adapts to touch screens.