# Geometry OpenVerbs Distance Calculator

> Geometry OpenVerbs Distance Calculator is a paid API for AI agents from geometry.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-16).

Computes Euclidean, Manhattan, and Chebyshev distances between two 2D points in a single call.

## Facts

- Endpoint: POST https://geometry.openverbs.com/v1/distance
- Price: $0.004/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/geometry-openverbs-distance-calculator-fadd4006
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_SnhcCkoT1NQO_Ft-JvrRv

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-openverbs-distance-calculator-fadd4006 -d '<json body>'
```

Example prompt: What's the Euclidean, Manhattan, and Chebyshev distance between the points (3, 4) and (9, 12)?

## When to prefer this

Choose this endpoint when you need all three classic 2D distance metrics (Euclidean, Manhattan, Chebyshev) in a single lightweight call, especially useful for comparing distance models side-by-side for pathfinding, clustering heuristics, or geometric analysis without writing custom math code.

## Known failure modes

- Missing 'from' or 'to' fields returns a 400 validation error
- Providing arrays with fewer or more than 2 numbers per point returns a schema validation error
- Non-numeric values in point arrays cause a type error
- Network timeouts or service unavailability return 5xx errors
- Insufficient payment balance triggers an x402 Payment Required response

## How this service works

Euclidean, Manhattan and Chebyshev distance between two 2-D points.

## Output

Returns numeric values for all three distance measures — Euclidean (straight-line), Manhattan (sum of absolute differences), and Chebyshev (maximum of absolute differences) — between the two provided 2D points.

## 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",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "required": [
      "from",
      "to"
     ],
     "properties": {
      "to": {
       "type": "array",
       "items": {
        "type": "number"
       },
       "maxItems": 2,
       "minItems": 2,
       "description": "End point [x, y]."
      },
      "from": {
       "type": "array",
       "items": {
        "type": "number"
       },
       "maxItems": 2,
       "minItems": 2,
       "description": "Start point [x, y]."
      }
     },
     "additionalProperties": false
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/geometry-openverbs-distance-calculator-fadd4006/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from geometry.openverbs.com](https://www.zero.xyz/host/geometry.openverbs.com/llms.txt)