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ForgeMesh Geometry API
x402
ForgeMesh Geometry API is a paid API for AI agents from x402.forgemesh.io, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-13).
Computes exact area, perimeter, volume, surface area, and diagonals for 2D and 3D geometric shapes from structured dimension inputs, with triangle inequality validation.
Price / call$0.002
Success—
StatusUnknown
How this service works
Geometry API: exact area, perimeter, volume, surface area, and diagonals for circles, rectangles, triangles (Heron's or base-height), spheres, cylinders, cones, cubes, and rectangular prisms — from structured dimensions. Validates the triangle inequality. For CAD, construction, education, and design agents.
Output
Returns exact numeric values for the relevant geometric properties of the specified shape — such as area, perimeter, volume, surface area, and diagonals — based on the shape type and provided dimensions. For triangles, also validates the triangle inequality.
Example use cases
Example prompt
“What's the volume and surface area of a cylinder with radius 4 and height 10? Also give me the area of its circular base.”
Technical details
Endpoint
POSThttps://x402.forgemesh.io/geometryWhen to prefer
Use this endpoint when you need mathematically exact geometric computations for standard 2D or 3D shapes without implementing formulas yourself — especially in CAD, construction planning, educational tools, or design workflows where precision matters. Prefer this over general-purpose math APIs when dealing specifically with geometric shapes and needing multiple properties (area + perimeter + diagonal) in a single call.
Side effects
- Missing required dimensions for the specified shape returns an error
- Invalid shape type string returns an unrecognized shape error
- Triangle sides that violate the triangle inequality return a validation failure
- Non-numeric string values for dimension fields cause parsing errors
- Omitting the 'shape' field results in an unprocessable request
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| a | string | |
| b | string | |
| c | string | |
| base | string | |
| side | string | |
| shape | string | circle|rectangle|triangle|sphere|cylinder|cone|cube|rectangular_prism |
| width | string | |
| height | string | |
| length | string | |
| radius | string |
Output
Schema · Response
{
"type": "json",
"example": {
"shape": "sphere",
"volume": 523.598776,
"surface_area": 314.159265
}
}Tags
x402
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