How far does a cell tower actually reach?

Every structure page on this site shows a figure called the radio horizon. It comes from one line of arithmetic, and it is worth understanding both what that line computes and what it deliberately ignores.

The formula

$$d \approx 4.12 \times \sqrt{h}$$

with height in metres and distance in kilometres. A 60-metre tower gives about 32 km. A 200-metre tower gives about 58 km. The 628-metre mast at Galesburg, North Dakota — the tallest registered structure in the country — gives about 103 km.

The square root is the important part. Doubling the height does not double the reach; it multiplies it by about 1.41. Going from 50 m to 100 m buys you roughly 12 more kilometres of horizon. Going from 300 m to 600 m buys you about 30. Height has diminishing returns, which is one reason extremely tall structures are rare outside broadcast.

Where the constant comes from

The pure geometric horizon on a sphere is about 3.57 × √h. If the earth were a smooth ball and radio travelled in perfectly straight lines, that would be the answer.

Radio does not travel in perfectly straight lines. The atmosphere is denser near the ground, its refractive index decreases with altitude, and this bends radio waves very slightly downward — following the curve of the earth a little. The standard engineering treatment is to pretend the earth is 4/3 its actual radius and keep the straight-line maths. That substitution turns 3.57 into 4.12.

This is a convention, not a law. It describes typical atmospheric conditions in temperate climates. Under a temperature inversion, signals can duct far beyond it — this is why distant broadcast stations sometimes appear on quiet nights. Under other conditions they fall short.

What it deliberately ignores

The formula takes exactly one input: height. It knows nothing about:

Transmit power. A 200 m mast running low power and a 200 m mast running high power give identical horizon figures and very different real coverage.

Frequency. Low-band signal at 700 MHz and millimetre wave at 28 GHz from the same structure behave completely differently — the first reaches most of the horizon, the second struggles past a few hundred metres.

Terrain. The formula assumes flat, unobstructed ground. A hill 5 km away ends the useful range at 5 km regardless of what the arithmetic says.

Buildings and foliage. In a city, useful range is frequently a few hundred metres. Trees in leaf attenuate significantly, which is why some rural links work noticeably better in winter.

Receiver height. Strictly the horizon depends on both ends. A receiver at ground level sees less than one on a rooftop. We assume ground level, which is the conservative case.

Antenna pattern. Real antennas are sectored and downtilted, aimed at a planned service area rather than at the horizon. The horizon is not the design target.

So why show it at all?

Because height is the one thing the public record actually gives us, and the relationship between height and reach is the single most useful thing you can derive from it.

The figure is honest about what it is: a ceiling. It answers “could a signal from the top of this structure conceivably reach my town?” — and when the answer is no, that is genuinely informative. When the answer is yes, it tells you only that distance is not the reason your signal is poor, which sends you to look at the more likely causes.

Every page that shows the figure says so in the same breath. We would rather show a labelled estimate than either a fake precision or nothing at all.

A worked example

Take a 100-metre lattice tower on flat ground.

• Radio horizon: 4.12 × √100 = 41 km
• Realistic rural coverage on low-band: perhaps 15–25 km
• Realistic suburban coverage on mid-band: perhaps 2–5 km
• Realistic urban coverage on C-band: perhaps 0.5–1.5 km
• Coverage inside a modern insulated building at the edge of any of those: often none

Same structure, same height, same number at the top of the page. The horizon figure is the widest of those five numbers by a wide margin, and that is exactly what a ceiling should be.