# Geometry Shape Measurements API

> Geometry Shape Measurements API is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Computes area, perimeter, surface area, and volume for 2D and 3D geometric shapes including circles, polygons, spheres, cylinders, cones, boxes, tori, and more.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/shape-measure?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/geometry-shape-measurements-api-1100d4de
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_wO4n5UE4y_AGu-t_Xe3YO

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability geometry-shape-measurements-api-1100d4de
```

Example prompt: Can you calculate the surface area and volume of a cylinder with radius 4 and height 9?

## When to prefer this

Choose this endpoint when you need fast, reliable geometric measurements for standard 2D or 3D shapes without writing your own math. Ideal for educational tools, engineering estimations, packaging calculations, or any agent workflow requiring computed geometry properties. Covers a broad range of shapes (14+) in a single API, avoiding the need to implement formulas manually.

## Known failure modes

- Missing required 'shape' query parameter returns an error
- Shape-specific required parameters not provided (e.g. radius missing for circle) result in an error
- Unsupported shape name returns an error or empty result
- Negative or zero dimensions may produce errors or undefined results
- Network or payment (x402) failure prevents response

## How this service works

Area, perimeter, surface area and volume of circles, polygons, sectors, spheres, cylinders, cones, boxes, tori and more.

## Output

Returns a JSON object containing the shape name, the input parameters used, computed measurements (area, perimeter, surface area, volume as applicable), a human-readable summary, and metadata such as source and timestamp.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "shape"
     ],
     "properties": {
      "R": {
       "type": "number",
       "description": "Torus major radius"
      },
      "a": {
       "type": "number",
       "description": "Semi-axis or side a"
      },
      "b": {
       "type": "number",
       "description": "Semi-axis or side b"
      },
      "c": {
       "type": "number",
       "description": "Semi-axis c"
      },
      "h": {
       "type": "number",
       "description": "Height"
      },
      "l": {
       "type": "number",
       "description": "Length (box)"
      },
      "r": {
       "type": "number",
       "description": "Radius (circle, sector, sphere, cylinder, cone, torus tube)"
      },
      "w": {
       "type": "number",
       "description": "Width"
      },
      "base": {
       "type": "number",
       "description": "Triangle base"
      },
      "side": {
       "type": "number",
       "description": "Polygon side length"
      },
      "shape": {
       "type": "string",
       "description": "circle, rectangle, triangle, ellipse, trapezoid, regular-polygon, sector, sphere, cylinder, cone, box, pyramid, torus or ellipsoid"
      },
      "sides": {
       "type": "integer",
       "description": "Polygon sides"
      },
      "height": {
       "type": "number",
       "description": "Triangle or trapezoid height"
      },
      "angleDeg": {
       "type": "number",
       "description": "Sector angle in degrees"
      },
      "baseArea": {
       "type": "number",
       "description": "Pyramid base area"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "shape": {
       "type": [
        "null",
        "string"
       ]
      },
      "inputs": {
       "type": [
        "null",
        "object"
       ],
       "properties":
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/geometry-shape-measurements-api-1100d4de/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)