GenerateRandomSearch

Random Point in Radius Generator

Picking a random angle and a random distance between zero and the radius is the obvious way to scatter points in a circle, and it is wrong: it puts as many points in the inner half of the radius as the outer half, even though the outer ring has three times the area. One square root fixes it. This generator does that, and reports the mean distance next to the two-thirds-of-the-radius figure a correct sampler tends towards — so you can see the property rather than take it on trust.

What this generator does

Draws a bearing and a distance for each point — the distance as the radius times the square root of a uniform value, which is what spreads points over area — and places the point with the spherical destination formula. Each point's distance from the centre is then measured back with the haversine formula.

How to use this tool

  1. Set the centre latitude and longitude, and the radius in kilometres.
  2. Choose how many points you need.
  3. Generate, and check the mean distance against the expected figure shown.
  4. Copy the results as CSV, or seed them to reproduce the same set.

Understanding the controls

How many points
Between 1 and 200. Around a hundred is enough for the mean distance to settle near its expected value.
Radius (km)
Up to 500 km. Larger radii are where a flat-earth approximation would start putting points outside the circle entirely.
Centre latitude
Between -85 and 85 degrees. The poles are excluded because the bearing at a pole is not well defined.
Centre longitude
Between -180 and 180 degrees. Circles that cross the date line are wrapped correctly rather than running past 180.
Seed
Reproduces the identical set of coordinates, which is what makes these usable as fixtures.

Common use cases

  • Test coordinates for a geofence, a proximity search or a delivery radius
  • Sample locations for a map or a mock dataset
  • Demonstrating why the obvious sampling method clusters at the centre
  • Generating points that stay inside a radius even at high latitudes
  • Producing the same set of coordinates twice from a seed

How this generator works

Distances use r = R√u, which gives a density proportional to area rather than to radius. Points are then placed with the spherical destination formula — adding flat north and east offsets instead put points up to 39 km outside a 500 km circle at 80 degrees north when it was measured. Every point is checked back against the centre before display.

Randomness and fairness

The bearings and distances are random; the even spread is a property of how the distance is drawn, and is measurable in the mean distance shown. Seeded sets reproduce exactly and are therefore explicitly not cryptographically secure. Unseeded, the browser's cryptographically secure generator is used.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • The Earth is treated as a sphere, so distances differ from ellipsoidal ones by a fraction of a percent.
  • Points can land in the sea, on a runway or inside a building — nothing here knows what is on the ground.
  • Latitudes beyond 85 degrees are refused, because bearings stop being meaningful near a pole.
  • The radius is a great-circle distance, not a driving or walking distance.
  • Coordinate sets are not stored between visits; seed one you need again.

Privacy and your data

Coordinates are generated and measured entirely in your browser. The centre you type, your seed and the points produced are never transmitted and never stored.

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