Coordinate systems: latitude and longitude

Before you can do any map math, you need a precise model of where a point is on Earth. Latitude and longitude are the coordinate systems every developer uses: a two-number address agreed on internationally and supported by virtually every GPS receiver, mapping API, and spatial database in existence.

The basics

• Latitude (φ): North-south, from −90° (South Pole) to +90° (North Pole). The equator is 0°.
• Longitude (λ): East-west, from −180° to +180°. The prime meridian (Greenwich) is 0°.

A point is written as (lat, lon) in most APIs (Google, Apple), but as [lon, lat] in GeoJSON (because GeoJSON follows the (x, y) convention). This trips up every developer at least once.

// Google Maps style:
const point = { lat: 31.5204, lng: 74.3587 }; // Lahore

// GeoJSON style:
const point = [74.3587, 31.5204]; // [lon, lat]

The reason GeoJSON uses [lon, lat] is that longitude is the east-west axis — analogous to x in a standard Cartesian plane — and latitude is north-south, analogous to y. Cartographers conventionally write (x, y) first, so GeoJSON follows that order. Most web APIs flip this to (lat, lon) because humans think of location as "how far north/south, then how far east/west."

Decimal degrees vs DMS

How big is a degree?

This is one of the most useful intuitions you can have. Drag the slider to see how 1° of longitude shrinks as you move toward the poles.

Quantity	Value
1° latitude	≈ 111.32 km (everywhere)
1° longitude	≈ 111.32 km × cos(latitude)

Latitude lines are evenly spaced. Longitude lines converge at the poles. So at 60° N, one degree of longitude is only ~55.7 km.

The convergence of longitude lines is why you can't use simple Pythagorean math to compute distances between two lat/lon points — the grid is not uniform. A 1° × 1° box near the equator is nearly square; the same box near the poles is a very thin sliver.

Formula for the length of 1° of longitude at latitude φ:

$$\text{length} = \frac{\pi}{180} \cdot R \cdot \cos(\varphi)$$

Q: How far apart are two points at the same latitude (51.5° N, London) but 1° apart in longitude?

$$\text{length} = \frac{\pi}{180} \cdot 6{,}371{,}008.8 \cdot \cos(51.5° \cdot \pi/180)$$ $$= 111{,}195 \times \cos(0.8988) = 111{,}195 \times 0.6225 \approx 69{,}222 \text{ m} \approx 69.2 \text{ km}$$

Datums (briefly)

A datum defines where (0, 0) sits and the shape of the reference ellipsoid. The Earth is not a perfect sphere — it bulges at the equator and flattens at the poles. A datum specifies the exact ellipsoid used, including its semi-major axis (equatorial radius) and flattening factor.

The dominant datum today is WGS84, used by GPS. Older maps may use NAD27, NAD83, OSGB36, etc. Coordinates can shift by tens to hundreds of meters between datums, so always know which one your data uses. A GPS coordinate in WGS84 can be 50–100 m away from the "same" location in a legacy national datum — enough to place a marker on the wrong building.

EPSG codes are standard identifiers:

• EPSG:4326 — WGS84 lat/lon (degrees)
• EPSG:3857 — Web Mercator (meters, used by Google/Bing/OSM tiles)