Line of Sight / Viewshed Radius Calculator

Line of sight is the uninterrupted path between an observer and a target. In a perfectly flat world, visibility would depend only on obstacles like buildings and terrain. On Earth, the curved surface itself eventually blocks the view, no matter how clear the air is. The line-of-sight distance calculator finds the maximum range where two points can still see each other, accounting for that curvature and the way the atmosphere bends light.

This matters for cell tower planning, where a 30-metre mast can reach handsets tens of kilometres away; for wind turbine siting, where aviation and radar visibility must be checked; for drone visual line-of-sight flights; and for hikers estimating how far they can see from a summit or fire tower.

How Earth's Curvature Limits How Far You Can See

Imagine standing on a perfectly smooth sphere. Your eye is a short distance above the surface, so the horizon is the point where your line of sight is tangent to the sphere. Beyond that tangent point, the surface curves away and hides everything behind it. If the target is also above the surface — another hill, a building, or a cell phone held at head height — it brings its own horizon closer, and the two horizons add together.

The exact formula for the tangent distance from a height h above a sphere of radius R is:

When the heights are small compared with Earth's radius, this simplifies to the well-known approximation d ≈ sqrt(2Rh). The calculator uses the exact form, so it stays accurate even for aircraft and high-altitude platforms.

Atmospheric Refraction: Why the Horizon Is Farther Than Geometry Suggests

Light from a distant object does not travel in a straight line through the atmosphere. Air density is higher near the ground, so rays bend downward slightly, following a curved path. The effect is the same as if Earth were a little larger than it really is. Surveyors and radio engineers model this with an effective Earth radius:

The coefficient k is typically about 0.13 for visible light on a standard day, giving an effective radius of roughly 7,320 km. Radio and microwave links often use k ≈ 0.25, equivalent to the common 4/3-Earth model. The calculator lets you switch between no refraction, standard visual refraction, and radio/microwave refraction, or enter your own k value.

Line-of-Sight Formula Explained

For two points at heights h₁ and h₂ above a smooth Earth with effective radius R_eff, the maximum straight-line visibility distance is the sum of the two tangent distances:

The ground arc distance along the surface is R_eff × (α₁ + α₂), where αᵢ = acos(R_eff / (R_eff + hᵢ)). For typical surface heights, the arc distance and the straight-line distance are nearly identical, but both are reported so engineers can use whichever their workflow requires.

Visible Horizon by Observer Height

The table below shows the visual horizon distance for a single observer on a standard day with k = 0.13. Set the target height to zero in the calculator to reproduce any of these values.

Common Uses: Cell Towers, Wind Turbines, Drones, and Hiking

Cell towers: A macro tower with a 30-metre antenna can theoretically see a handset at 1.5 metres above ground out to about 25 kilometres on a standard day. Real coverage is smaller because terrain, buildings, and vegetation block the path, but the geometric limit is the starting point.

Wind turbines: Aviation authorities and radar operators need to know whether a turbine hub or blade tip will break the line of sight to a radar or navigation aid. The calculator gives the worst-case geometric visibility.

Drones: Many jurisdictions require the pilot to keep the drone within visual line of sight. Enter the drone altitude and the pilot's eye height to check the regulatory margin.

Hiking and mountaineering: From a 2-metre eye level on flat terrain, the horizon is only about 5 kilometres away. Climb to 600 metres and it stretches to roughly 94 kilometres — a useful rule of thumb for estimating what peaks should be visible.

Frequently Asked Questions