# Cartograph True Size of Countries (Mercator comparer)

> Move a country to another latitude and see its true size against the Mercator map. Moves a country outline (Natural Earth admin-0) to any place on the globe while keeping its true shape and area, and shows how big it looks on a Web-Mercator map at home and at the new place, next to its real geodesic area and an optional second country. It is the true-size engine of the Cartograph app.

Part of usefulweb.app (https://usefulweb.app/). Part of [Cartograph](https://cartograph.usefulweb.app/) (ownerApp: cartograph). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://cartographtruesize.usefulweb.app/ (interactive tool at https://cartographtruesize.usefulweb.app/tool)
- JSON API: POST https://cartographtruesize.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://cartographtruesize.usefulweb.app/api/v1/tool)
- OpenAPI: https://cartographtruesize.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://cartographtruesize.usefulweb.app/mcp - tool `cartograph_true_size`

## Inputs
- country (text): Country (English name or ISO code)
- target (text): Move it to - Coordinate of the new centre (anchor = centre of the bounding box of the largest part).
- rotationDeg (number): Rotation (clockwise)
- compare (text): Compare with (optional) - A second country drawn at home and compared by true area.

## Method
- Outlines: Natural Earth 1:110m admin-0 countries (public domain), the same file as the Geo Data Visualizer; small countries and islands below that scale are missing.
- Moving: every vertex keeps its geodesic distance and azimuth from the anchor (Karney’s inverse problem at home, direct problem at the new place, WGS84). On a sphere this is an exact rotation; on the ellipsoid the true area changes by well under 1 % — both areas are reported.
- True area: geodesic polygon area on WGS84 (outer rings minus holes). Apparent area: planar area of the outline in Web Mercator at equator scale, which grows with sec²(latitude) — 4 × at 60°.