County Maps US

Tools Distance, area and drive time

Horizon Distance Calculator

Enter a height above the ground and the tool returns the geometric and refracted horizon distance, and draws the visible circle from your chosen point.

How to use it

  1. Enter your eye height above the surrounding ground or sea, in feet or metres. On a hill or tower, include the hill or tower.
  2. Optionally type where you are, use your location, or click the map.
  3. Press Calculate. The horizon distance with and without refraction, the dip angle and the circle on the map appear, with a list of US towns inside the circle.

How it works

The geometric horizon is the tangent distance sqrt(2Rh + h²) with R = 6,371 km. Light bends slightly around the Earth in a standard atmosphere, so the refracted horizon uses an effective radius of 7/6 R, the usual surveying convention; this matches the 3.86 × √h km rule of thumb and is typically 8 percent further. The dip of the horizon is arccos(R / (R + h)) for each case. All of it is computed in the browser.

The circle drawn is the sea-level horizon around the observer; terrain is not checked, so a hill in between still blocks the view and a tall object beyond the circle can still be seen. The list of places inside the circle comes from a Census-derived file of US places with 10,000 or more people shipped with this site, and shows only places whose centre is closer than the horizon.

Questions

How far away is the horizon?
For a person standing on a beach, eye about 5.5 feet up, the sea horizon is about 2.9 miles away, or 3.1 miles with refraction. From 100 feet it is about 12 to 13 miles; from a 35,000 foot flight, about 230 to 250 miles.
Why are there two answers?
The geometric figure assumes light travels in straight lines. In the real atmosphere light bends down slightly, which lets you see a little beyond the geometric horizon; the refracted figure allows for that under average conditions. Hot or cold air can change it either way.
Can I see a city that is inside the circle?
Only if nothing is in the way and the city is tall enough to stand above your horizon. The list is based on distance alone, so use it as a candidate list and check the terrain between.

All map tools, free and without an account. Location data is processed in your browser and by the open geocoding services named on the sources page; nothing is stored by this site.