Math & Scientific
Quadratic Formula Calculator
Quadratic Formula: it solves ax² + bx + c = 0 with the quadratic formula x = (−b ± √(b²−4ac)) / 2a and reports the discriminant. Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
Quadratic Formula Calculator turns your a, b and c into the real or complex roots using the quadratic formula and discriminant. The maths runs locally, so nothing you enter leaves the page.
About this calculator
It solves ax² + bx + c = 0 with the quadratic formula x = (−b ± √(b²−4ac)) / 2a and reports the discriminant. It matters when you need the exact relationship checked quickly rather than worked through by hand. Worked below as Solve x² − 5x + 6 = 0: x = (5 ± √(25−24)) ÷ 2 = (5 ± 1) ÷ 2, so x = 3 or 2 . — and the calculator on this page repeats exactly that working for your inputs, instantly, and offline after load.
How to use
- Enter the coefficients a, b, and c from a x^2 + b x + c = 0.
- Make sure a is not zero, otherwise the equation is not quadratic.
- Press Calculate to apply the quadratic formula.
- Read the roots and the discriminant, which tells you how many real roots there are.
Why use Quadratic Formula Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Based on standard, well-established formulas.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it for quick mental-math cross-checks
Use it for double-checking a spreadsheet result
Use it for homework and assignment checks
Quadratic Formula in competitive-exam practice
Use it when revising for exams
Quadratic Formula in tutoring and teaching sessions
Technical notes
Quadratic Formula Calculator solves ax² + bx + c = 0 with the quadratic formula x = (−b ± √(b²−4ac)) / 2a and reports the discriminant.
Inputs are taken exactly as entered, so check for typos before trusting an answer.
All arithmetic runs in your browser using double-precision floating point, so extreme inputs may show tiny rounding differences.
FAQ
What does the discriminant tell me?
The discriminant b^2 - 4ac shows the nature of the roots: positive gives two real roots, zero gives one repeated root, and negative gives a pair of complex roots.
Why can't a be zero?
If a is zero there is no x^2 term, so the equation is linear rather than quadratic and the quadratic formula does not apply.
Does it show complex roots?
Yes. When the discriminant is negative, the calculator reports the two complex roots in a plus or minus bi form.
Does the Quadratic Formula Calculator send my data to a server?
No. The Quadratic Formula Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
Solve x² − 5x + 6 = 0: x = (5 ± √(25−24)) ÷ 2 = (5 ± 1) ÷ 2, so x = 3 or 2.