# Circle intersection calculator - Human page: https://happytails.ai/en/calculators/circle-intersection-calculator/ - Markdown: https://happytails.ai/en/calculators/circle-intersection-calculator.md - Structured JSON: https://happytails.ai/agents/en/calculators/circle-intersection-calculator/index.json - Visibility: public ## Tool capabilities | Property | Value | | --- | --- | | Tool ID | `circle-intersection-calculator` | | Category | calculators | | Implementation | Registered implementation. Registration alone is not a production-quality guarantee. | | Browser execution | Automatic updates after valid input or file selection. | | Browser processing | Browser; see tool notes for network behavior. | | HTTP API | Not callable through HTTP. | | Browser-agent interface | run_current_tool | ### Implementation notes Use the same unit for coordinates and radii. Positive Y points up; overlap area uses square units. Calculations use floating-point arithmetic. Cases within the reported numerical tolerance are treated as tangent. Zero-radius circles represent points. Your input stays on your device. ### Inputs and settings No free-text input is required. Use the file inputs and/or settings below. | Setting | Meaning | Control type | Default | Constraints | | --- | --- | --- | --- | --- | | `x1` | First center X | number | 0 | min=-1000000000 max=1000000000 step=any | | `y1` | First center Y | number | 0 | min=-1000000000 max=1000000000 step=any | | `radius1` | First radius | number | 1 | min=0 max=1000000000 step=any | | `x2` | Second center X | number | 1 | min=-1000000000 max=1000000000 step=any | | `y2` | Second center Y | number | 0 | min=-1000000000 max=1000000000 step=any | | `radius2` | Second radius | number | 1 | min=0 max=1000000000 step=any | ### Browser-agent workflow 1. Open the human page in a browser that supports WebMCP. 2. Discover the interface exposed by that page; use its actual schema. 3. Select files on the page first when the tool requires files. 4. Call `run_current_tool` with valid input and settings. 5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links. Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution. ### Planning specification Use the same measurement unit for every coordinate and radius. Coordinates must be finite with magnitudes up to 1,000,000,000. A radius may be zero or between 0.000000001 and 1,000,000,000. Positive Y points up. Results use floating-point arithmetic, not exact symbolic geometry. Cases within the displayed numerical tolerance are treated as tangent; overlap area is measured in the square of your coordinate unit. Coincident circles have infinitely many intersections, represented explicitly rather than as a fabricated point list. This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support. ### Complete machine-readable capability record ```json { "id": "circle-intersection-calculator", "category": "calculators", "built": true, "requirements": "Use the same measurement unit for every coordinate and radius. Coordinates must be finite with magnitudes up to 1,000,000,000. A radius may be zero or between 0.000000001 and 1,000,000,000. Positive Y points up. Results use floating-point arithmetic, not exact symbolic geometry. Cases within the displayed numerical tolerance are treated as tangent; overlap area is measured in the square of your coordinate unit. Coincident circles have infinitely many intersections, represented explicitly rather than as a fabricated point list.", "implementation": { "fields": [ { "key": "x1", "label": "First center X", "value": 0, "type": "number", "min": -1000000000, "max": 1000000000, "step": "any" }, { "key": "y1", "label": "First center Y", "value": 0, "type": "number", "min": -1000000000, "max": 1000000000, "step": "any" }, { "key": "radius1", "label": "First radius", "value": 1, "type": "number", "min": 0, "max": 1000000000, "step": "any" }, { "key": "x2", "label": "Second center X", "value": 1, "type": "number", "min": -1000000000, "max": 1000000000, "step": "any" }, { "key": "y2", "label": "Second center Y", "value": 0, "type": "number", "min": -1000000000, "max": 1000000000, "step": "any" }, { "key": "radius2", "label": "Second radius", "value": 1, "type": "number", "min": 0, "max": 1000000000, "step": "any" } ], "input": false, "live": true, "presentation": "metrics", "note": "Use the same unit for coordinates and radii. Positive Y points up; overlap area uses square units. Calculations use floating-point arithmetic. Cases within the reported numerical tolerance are treated as tangent. Zero-radius circles represent points. Your input stays on your device.", "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.", "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 Find where two circles meet and measure their overlap. Enter both centers and radii, then download the diagram and intersection coordinates. How can we improve this tool? Report a problem or share an idea. Please leave out private information. Your message and the tool name go to our team via PostHog. ### How to use Circle intersection calculator 1. Enter the X and Y coordinates of each center and both radii. 2. Read the relationship, intersection count and overlap area. The diagram uses one scale for both circles. 3. Download the intersection points as CSV, the full calculation as JSON or the diagram as SVG. ## Useful next steps - [Graphing calculator](https://happytails.ai/en/calculators/graphing-calculator/) ([Markdown](https://happytails.ai/en/calculators/graphing-calculator.md)) - [Bolt circle calculator](https://happytails.ai/en/calculators/bolt-circle-calculator/) ([Markdown](https://happytails.ai/en/calculators/bolt-circle-calculator.md)) - [Length](https://happytails.ai/en/unit-converters/length/) ([Markdown](https://happytails.ai/en/unit-converters/length.md)) ## Two circles, one coordinate system Use the same unit for all six inputs. For two unit circles centered at (0, 0) and (1, 0), the intersections are (0.5, 0.8660254…) and (0.5, -0.8660254…). The overlap area is approximately 1.2283697 square units. ### Handle every relationship Separated circles have no shared area. Contained circles have the area of the smaller circle in common. Tangent circles meet at one point. Identical nonzero circles share infinitely many points. A zero-radius circle is treated as one point. ### Keep precision in the download The visible result uses localized display numbers. CSV and JSON preserve the calculated numeric values. The numerical tolerance is based on floating-point precision and the scale of the circles; this is not exact symbolic geometry.