Coordinate transforms — converting between CRS

A coordinate reference system (CRS) defines how coordinates map to a location on Earth. Most data you encounter is in one of two CRS, and converting between them is a daily task.

The two you'll use 95% of the time

The distinction matters in practice because operations that assume planar geometry — computing buffer distances, calculating area, overlaying rasters — work correctly in metres but give wrong results in degrees. A degree of longitude at the equator is ~111 km; a degree of longitude at 60°N is ~56 km. Treating them as equal without projection introduces systematic distortion.

EPSG:4326 → EPSG:3857 (degrees → metres)

This is the Mercator projection formula you saw in Chapter 4, applied to the Web Mercator sphere:

where $R = 6{,}378{,}137$ m (WGS84 equatorial radius), and φ, λ are in radians.

const R = 6_378_137; // metres

function toWebMercator(lat, lon) {
  const x = (lon * Math.PI / 180) * R;
  const y = Math.log(Math.tan(Math.PI / 4 + (lat * Math.PI / 180) / 2)) * R;
  return { x, y };
}

EPSG:3857 → EPSG:4326 (metres → degrees)

The inverse:

function fromWebMercator(x, y) {
  const lon = (x / R) * (180 / Math.PI);
  const lat = (2 * Math.atan(Math.exp(y / R)) - Math.PI / 2) * (180 / Math.PI);
  return { lat, lon };
}

Valid range for Web Mercator

Web Mercator cannot represent the poles. The practical limits are:

• Longitude: −180° to +180°
• Latitude: −85.051129° to +85.051129°

At exactly ±90°, the formula produces ±∞ in the y direction. Google Maps and friends clip to ±85.051129° to produce a square world tile.

Using proj4js

For anything beyond 4326 ↔ 3857, use proj4:

npm install proj4

import proj4 from "proj4";

// Define your custom CRS (find definitions at epsg.io)
proj4.defs("EPSG:32642", "+proj=utm +zone=42 +datum=WGS84 +units=m +no_defs");

// Convert Lahore from WGS84 to UTM Zone 42N
const [easting, northing] = proj4("EPSG:4326", "EPSG:32642", [74.3587, 31.5204]);
// → [381453, 3488694]  (metres from zone origin)