Random Location Generator

How True Area-Weighted Spherical Random Sampling Works

This random location generator picks mathematically unbiased GPS coordinates across World Land, the United States (50 states and D.C.), or any individual U.S. state by weighting every candidate polygon ring by its true spherical surface area and sampling latitude via arcsin before running a point-in-polygon check. Every square mile of land inside your chosen scope has the exact same probability of being selected.

Why Naive Latitude and Longitude Randomizers Are Biased Toward the Poles

Many simple coordinate generators pick a random latitude uniformly between −90° and +90° and a random longitude between −180° and +180°. Because lines of longitude converge at the North and South Poles, the east-west width of 1° of longitude shrinks by cos(φ): a 1° × 1° grid cell at 70°N in northern Alaska has only 34% of the land area of a 1° × 1° cell at the Equator, and a cell at 85°N has less than 9%. Uniform degree sampling therefore crowds far too many points into high latitudes.

Our Three-Step Geodesic Rejection Sampling Pipeline

• Step 1 — Spherical Bounding-Box Weighting: Each polygon ring in our U.S. Census Bureau state boundary dataset or Natural Earth 1:50m world land dataset is weighted by its spherical zone area proportional to (λmax − λmin) × (sin φmax − sin φmin), so larger landmasses and states (such as Alaska, Texas, and California in the U.S. scope) are chosen in exact proportion to their real-world area.
• Step 2 — Uniform sin(φ) Draw: Within the selected bounding box, longitude λ is drawn uniformly and latitude is computed as φ = arcsin(u) where u is uniform between sin(φmin) and sin(φmax).
• Step 3 — Ray-Casting Polygon & Nearest-Place Lookup: The candidate point is verified against the exact polygon ring (including interior holes), and for U.S. points we also look up the nearest incorporated city or town from our 32,642-place Census index.