# Polygon measures compute

`polygon-measures-compute` · version 1.0.0 · Other utilities · free, no key needed

Compute exact signed double-area, area, orientation, and squared edge lengths for a rational simple polygon.

**Use when you need to: compute exact polygon area · shoelace formula for rational coordinates · find polygon orientation.**

## Decide before calling

Read the [versioned contract](/v1/tools/polygon-measures-compute/versions/1.0.0) and the supported scope below. Reuse `polygon-measures-compute@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `polygon-measures-compute@1.0.0` for compute exact polygon area. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- compute exact polygon area
- shoelace formula for rational coordinates
- find polygon orientation
- calculate signed double area
- squared lengths of polygon edges
- measure a simple polygon exactly
- polygon area without floating point

## Not supported

- self-intersecting or degenerate polygons
- square-root perimeter approximation
- three-dimensional or curved geometry

## Behavior

- Vertices are ordered boundary vertices; the closing edge from the last vertex to the first is implicit.
- Coordinates must be canonical reduced base-10 integers or p/q fractions with positive denominators and components no larger than 1000000000000000000.
- The polygon must be simple and nondegenerate; signed double-area is positive for counterclockwise order and negative for clockwise order.
- Area and each squared edge length are exact reduced rational strings; no floating-point approximation or rounding occurs.
- perimeter_squared_components follows edge order and includes the closing edge; it reports squared lengths rather than irrational square roots.

## Input

- `vertices` (array of object, required): min items 3; max items 128

## Output

- `signed_double_area` (string, required): min length 1; max length 256; pattern `^-?(0|[1-9][0-9]*)(/[1-9][0-9]*)?$`
- `absolute_area` (string, required): min length 1; max length 256; pattern `^(0|[1-9][0-9]*)(/[1-9][0-9]*)?$`
- `orientation` (one of "counterclockwise", "clockwise", required)
- `perimeter_squared_components` (array of string, required): min items 3; max items 128; each min length 1; each max length 256; each pattern `^(0|[1-9][0-9]*)(/[1-9][0-9]*)?$`

## Limits

- max input bytes: 20000
- max vertices: 128
- max coordinate bytes: 64
- max abs integer component: 1000000000000000000
- max output bytes: 40000

## Example

Request input:

```json
{
  "vertices": [
    {
      "x": "0",
      "y": "0"
    },
    {
      "x": "4",
      "y": "0"
    },
    {
      "x": "0",
      "y": "3"
    }
  ]
}
```

Response:

```json
{
  "result": {
    "signed_double_area": "12",
    "absolute_area": "6",
    "orientation": "counterclockwise",
    "perimeter_squared_components": [
      "16",
      "25",
      "9"
    ]
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "polygon-measures-compute",
  "version": "1.0.0",
  "input": {
    "vertices": [
      {
        "x": "0",
        "y": "0"
      },
      {
        "x": "4",
        "y": "0"
      },
      {
        "x": "0",
        "y": "3"
      }
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/polygon-measures-compute/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"vertices":[{"x":"0","y":"0"},{"x":"4","y":"0"},{"x":"0","y":"3"}]}'
```

The machine-readable contract is at [/v1/tools/polygon-measures-compute/versions/1.0.0](/v1/tools/polygon-measures-compute/versions/1.0.0).

### CLI

```sh
node cli.mjs run polygon-measures-compute 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Geohash convert](/tools/geohash-convert): Encode decimal coordinates as a bounded Geohash or decode a Geohash to its exact bounding box and midpoint.
- [Xlsx to CSV](/tools/xlsx-to-csv): convert excel sheet to csv.
- [Xlsx to markdown](/tools/xlsx-to-markdown): convert excel workbook to markdown.
- [Har summarize](/tools/har-summarize): Summarize a HAR 1.2 JSON log into deterministic request, status, MIME, host, timing, size, and redaction counts.
- [Hebrew civil date convert](/tools/hebrew-civil-date-convert): Convert dates between proleptic Gregorian calendar and civil Hebrew calendar
- [Rtf inspect](/tools/rtf-inspect): Inspect an 8 KiB ANSI-1252 RTF text subset: paragraphs, omitted destinations, pictures, objects and warnings.