{
  "title": "Graphing calculator",
  "human_url": "https://happytails.ai/en/calculators/graphing-calculator/",
  "agent_url": "https://happytails.ai/agents/en/calculators/graphing-calculator/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/graphing-calculator.md",
  "content": "Graphing calculator\nPlot functions, explore intersections and download a graph or table of values.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Graphing calculator\nEnter one function of x per line, such as x^2 and 2*x+3. Use explicit multiplication, parentheses and the supported functions listed in the calculator.\nChoose radians or degrees and adjust the window. Plot the functions, zoom or pan, then inspect numerical intersections in the visible range.\nSet a table start, end and step to inspect values. Download the SVG graph or the CSV table; check undefined values and sampling limitations before using the results.\nUseful next steps\nScientific calculator\nHow Graphing calculator works\nThis graphing calculator plots up to six real-valued functions of x, one per line, in a window you set with x and y limits, then lets you pan, zoom and read numerical intersections for each pair of functions. Curves are sampled at 1,024 intervals across the x range, and crossings are found from sign changes refined by bisection, plus a check for touching points. Features narrower than the sampling step can be missed. You also get a values table of up to 2,000 rows and downloads of the graph as SVG and the table as CSV. Everything runs in your browser.\nBefore you start\nWrite multiplication explicitly, such as 2*x rather than 2x, and check the angle unit, which starts in radians, before plotting trig functions. Choose an x range that contains the behavior you care about, because intersections are only searched inside it.\nA worked example\nPlotting x^2 and 2*x+3 in the default window from -5 to 5 lists intersections at (-1, 1) and (3, 9). Plotting sin(x) and cos(x) from -6.283 to 6.283 in radians finds four crossings, including x ≈ 0.7853981634, y ≈ 0.7071067812.\nWhat to expect\nPlot functions, explore intersections and download a graph or table of values. Plot up to six real-valued functions of x. Pan, zoom and set an exact viewing window. Inspect numerical intersections in that window and generate up to 2,000 table rows. Calculations stay on your device. Numerical sampling can miss features outside the range or narrower than the sampling interval, and intersections are estimates rather than symbolic solutions.\nCommon questions\nHow do I find where two graphs intersect?\nEnter both functions on separate lines and plot them. The Intersections section lists each crossing it finds within the current x range, to 10 significant digits. To find the x-intercepts of a single function, add 0 as a second line. Results are numerical estimates, so narrow the range to check close or clustered points.\nWhy do I get an error for 2x or sin x?\nThe calculator needs explicit multiplication and parentheses. Write 2*x instead of 2x, 3*sin(x) instead of 3sin(x), and sin(x) instead of sin x. The same applies to constants, so write 2*pi. You can start a line with y = if you like, but each line must be a function of x.\nShould I graph in degrees or radians?\nThe angle unit starts in radians, where sin(x) repeats every 2 × pi, about 6.283 units, so the default window shows under two cycles. In degrees, one cycle takes 360 units, so set the x range to something like 0 to 360 or the curve looks almost flat.\nWhy is part of my graph missing?\nThe calculator draws only real values. sqrt(x) has no real value for negative x, 1/x is undefined at 0 and ln(x) needs x above 0, so those parts are left out, and the CSV shows blank cells there. A curve can also leave the visible window, so widen the y limits or zoom out.\nDoes it solve equations exactly?\nNo. It samples the functions and estimates crossings numerically. It does not simplify expressions or prove that every intersection was found, and it lists at most 100 points per pair of functions. Use the results as close approximations, and check critical answers algebraically.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Scientific calculator",
      "url": "https://happytails.ai/en/calculators/scientific-calculator/"
    }
  ],
  "tool": {
    "id": "graphing-calculator",
    "category": "calculators",
    "built": true,
    "requirements": "Plot up to six real-valued functions of x. Pan, zoom and set an exact viewing window. Inspect numerical intersections in that window and generate up to 2,000 table rows. Calculations stay on your device. Numerical sampling can miss features outside the range or narrower than the sampling interval, and intersections are estimates rather than symbolic solutions.",
    "implementation": {
      "fields": [],
      "input": false,
      "note": "Plot real-valued functions, inspect numerical intersections and download a graph or values table. Calculations stay in your browser.",
      "experience": {
        "automatic": false,
        "single": false,
        "inputMaxLength": 1000000,
        "inputMode": "text",
        "label": "Your text",
        "placeholder": "Type or paste your input…",
        "help": "Up to 1,000,000 characters. Review the settings before running.",
        "action": null
      },
      "mode": "explicit",
      "interactive": true
    },
    "execution": "Browser interface",
    "api": null,
    "browser_agent": {
      "supported": false,
      "name": null,
      "discovery": "WebMCP on the human page in a supporting browser",
      "verification": "See audit/API-AUDIT.md; availability is not verification"
    }
  },
  "markdown": "# Graphing calculator\n\n- Human page: https://happytails.ai/en/calculators/graphing-calculator/\n- Markdown: https://happytails.ai/en/calculators/graphing-calculator.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/graphing-calculator/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `graphing-calculator` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Use the visible action or interactive controls. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | No callable WebMCP interface. |\n\n### Implementation notes\n\nPlot real-valued functions, inspect numerical intersections and download a graph or values table. Calculations stay in your browser.\n\n### Inputs and settings\n\nNo free-text input is required. Use the file inputs and/or settings below.\n\nNo additional settings are declared for this tool.\n\n### Planning specification\n\nPlot up to six real-valued functions of x. Pan, zoom and set an exact viewing window. Inspect numerical intersections in that window and generate up to 2,000 table rows. Calculations stay on your device. Numerical sampling can miss features outside the range or narrower than the sampling interval, and intersections are estimates rather than symbolic solutions.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"graphing-calculator\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Plot up to six real-valued functions of x. Pan, zoom and set an exact viewing window. Inspect numerical intersections in that window and generate up to 2,000 table rows. Calculations stay on your device. Numerical sampling can miss features outside the range or narrower than the sampling interval, and intersections are estimates rather than symbolic solutions.\",\n  \"implementation\": {\n    \"fields\": [],\n    \"input\": false,\n    \"note\": \"Plot real-valued functions, inspect numerical intersections and download a graph or values table. Calculations stay in your browser.\",\n    \"experience\": {\n      \"automatic\": false,\n      \"single\": false,\n      \"inputMaxLength\": 1000000,\n      \"inputMode\": \"text\",\n      \"label\": \"Your text\",\n      \"placeholder\": \"Type or paste your input…\",\n      \"help\": \"Up to 1,000,000 characters. Review the settings before running.\",\n      \"action\": null\n    },\n    \"mode\": \"explicit\",\n    \"interactive\": true\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": false,\n    \"name\": null,\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nPlot functions, explore intersections and download a graph or table of values.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Graphing calculator\n\n1. Enter one function of x per line, such as x^2 and 2\\*x+3. Use explicit multiplication, parentheses and the supported functions listed in the calculator.\n2. Choose radians or degrees and adjust the window. Plot the functions, zoom or pan, then inspect numerical intersections in the visible range.\n3. Set a table start, end and step to inspect values. Download the SVG graph or the CSV table; check undefined values and sampling limitations before using the results.\n\n## Useful next steps\n\n- [Scientific calculator](https://happytails.ai/en/calculators/scientific-calculator/) ([Markdown](https://happytails.ai/en/calculators/scientific-calculator.md))\n\n## How Graphing calculator works\n\nThis graphing calculator plots up to six real-valued functions of x, one per line, in a window you set with x and y limits, then lets you pan, zoom and read numerical intersections for each pair of functions. Curves are sampled at 1,024 intervals across the x range, and crossings are found from sign changes refined by bisection, plus a check for touching points. Features narrower than the sampling step can be missed. You also get a values table of up to 2,000 rows and downloads of the graph as SVG and the table as CSV. Everything runs in your browser.\n\n### Before you start\n\nWrite multiplication explicitly, such as 2\\*x rather than 2x, and check the angle unit, which starts in radians, before plotting trig functions. Choose an x range that contains the behavior you care about, because intersections are only searched inside it.\n\n### A worked example\n\nPlotting x^2 and 2\\*x+3 in the default window from -5 to 5 lists intersections at (-1, 1) and (3, 9). Plotting sin(x) and cos(x) from -6.283 to 6.283 in radians finds four crossings, including x ≈ 0.7853981634, y ≈ 0.7071067812.\n\n## What to expect\n\nPlot functions, explore intersections and download a graph or table of values. Plot up to six real-valued functions of x. Pan, zoom and set an exact viewing window. Inspect numerical intersections in that window and generate up to 2,000 table rows. Calculations stay on your device. Numerical sampling can miss features outside the range or narrower than the sampling interval, and intersections are estimates rather than symbolic solutions.\n\n## Common questions\n\n### How do I find where two graphs intersect?\n\nEnter both functions on separate lines and plot them. The Intersections section lists each crossing it finds within the current x range, to 10 significant digits. To find the x-intercepts of a single function, add 0 as a second line. Results are numerical estimates, so narrow the range to check close or clustered points.\n\n### Why do I get an error for 2x or sin x?\n\nThe calculator needs explicit multiplication and parentheses. Write 2\\*x instead of 2x, 3\\*sin(x) instead of 3sin(x), and sin(x) instead of sin x. The same applies to constants, so write 2\\*pi. You can start a line with y = if you like, but each line must be a function of x.\n\n### Should I graph in degrees or radians?\n\nThe angle unit starts in radians, where sin(x) repeats every 2 × pi, about 6.283 units, so the default window shows under two cycles. In degrees, one cycle takes 360 units, so set the x range to something like 0 to 360 or the curve looks almost flat.\n\n### Why is part of my graph missing?\n\nThe calculator draws only real values. sqrt(x) has no real value for negative x, 1/x is undefined at 0 and ln(x) needs x above 0, so those parts are left out, and the CSV shows blank cells there. A curve can also leave the visible window, so widen the y limits or zoom out.\n\n### Does it solve equations exactly?\n\nNo. It samples the functions and estimates crossings numerically. It does not simplify expressions or prove that every intersection was found, and it lists at most 100 points per pair of functions. Use the results as close approximations, and check critical answers algebraically.\n"
}