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Quadratic formula calculator

Open Quadratic formula calculator on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "id": "quadratic-formula",
  "category": "calculators",
  "built": true,
  "requirements": "If a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.",
  "implementation": {
    "fields": [
      {
        "key": "a",
        "label": "Coefficient a",
        "value": 1,
        "type": "number",
        "min": -1e+100,
        "max": 1e+100,
        "step": "any"
      },
      {
        "key": "b",
        "label": "Coefficient b",
        "value": -5,
        "type": "number",
        "min": -1e+100,
        "max": 1e+100,
        "step": "any"
      },
      {
        "key": "c",
        "label": "Coefficient c",
        "value": 6,
        "type": "number",
        "min": -1e+100,
        "max": 1e+100,
        "step": "any"
      }
    ],
    "input": false,
    "live": true,
    "presentation": "metrics",
    "note": "Solves ax² + bx + c = 0, including complex roots and linear cases. Uses a numerically stable real-root calculation. Floating-point results are rounded to 12 significant digits.",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 1000000,
      "inputMode": "text",
      "label": "Your text",
      "placeholder": "Type or paste your input…",
      "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
      "helpParts": [
        "Change the input or settings to update your result.",
        "Results update as you type.",
        "Up to 1,000,000 characters."
      ],
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}

Page guide

Solve a quadratic, including complex and repeated roots.

How to use Quadratic formula calculator
  1. Enter the values you want to calculate and choose the relevant units or settings.
  2. The result updates as you type. Adjust the available settings if needed.
  3. Review the result, then use Copy result or a download link when available.

Useful next steps

Scientific calculatorSlope calculatorPythagorean theorem calculator

How to use it

Write the equation as ax² + bx + c = 0, then enter its three coefficients. The discriminant b² - 4ac tells you whether the roots are real, repeated or complex.

A worked example

For x² - 5x + 6 = 0, enter 1, -5 and 6. The roots are 2 and 3. For x² + 1 = 0, the roots are i and -i.

What to know

If a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.