Formula and method
This calculator uses the values you enter and applies the calculation immediately in your browser. The main output formulas are:
- Discriminant (b²-4ac):
b*b-4*a*c - Root 1 (real, if discriminant ≥ 0):
a===0 ? NaN : (-b+Math.sqrt(Math.max(0,b*b-4*a*c)))/(2*a) - Root 2 (real, if discriminant ≥ 0):
a===0 ? NaN : (-b-Math.sqrt(Math.max(0,b*b-4*a*c)))/(2*a) - Real part (if discriminant < 0):
a===0 ? NaN : -b/(2*a) - Imaginary part ±(if discriminant < 0):
a===0 ? NaN : Math.sqrt(Math.max(0,-(b*b-4*a*c)))/(2*a)
Some formulas are undefined for certain input combinations, such as division by zero, equal x-values in a slope calculation, or logarithms of non-positive numbers. In those cases the live tool reports that the result is undefined instead of displaying Infinity or NaN.
Examples
- Example: with a = 1, b = -3, c = 2, this calculator returns Discriminant (b²-4ac) = 1, Root 1 (real, if discriminant ≥ 0) = 2, Root 2 (real, if discriminant ≥ 0) = 1, Real part (if discriminant < 0) = 1.5, Imaginary part ±(if discriminant < 0) = 0.
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Frequently asked questions
Is Quadratic Formula Calculator free to use?
Yes. Quadratic Formula Calculator is completely free, has no usage limit, and does not require an account, email, or API key.
Does Quadratic Formula Calculator store or upload my data?
No. Quadratic Formula Calculator calculates everything locally in your browser. Nothing you type is sent to a server or stored by SpecWhale.
How accurate is Quadratic Formula Calculator?
Quadratic Formula Calculator uses a standard formula (see the Method section above for the exact expression). For high-stakes financial, medical, or legal decisions, confirm the result with a professional or an authoritative source before relying on it.
Can I embed Quadratic Formula Calculator on my own website?
Yes. Use the "Embed this tool" snippet on this page to add a free, working copy of Quadratic Formula Calculator to your own blog post or page.
SEO and sharing notes
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