Radio Horizon: How Far VHF and UHF Signals Really Reach

Why does a 5 watt handheld reach a repeater twenty kilometres away from one hilltop but fail across a town from the bottom of a valley? Why does a station with a modest antenna on a tall mast beat a high-power station in a basement? The answer is the radio horizon. On VHF, UHF and the microwave bands, signals travel mostly in straight lines, and the curve of the earth and the terrain in the way decide how far they go. Antenna height matters more than almost anything else, and the calculation is simple enough to do in your head. This guide explains the radio horizon, gives the formula and a table of typical distances, shows what else steals range, and lists practical ways to extend it.

What the Radio Horizon Is

The earth is curved, so a transmitting antenna and a receiving antenna at ground level eventually drop out of sight of each other. The distance at which they can no longer see each other directly is the horizon. For light, it is the optical horizon. For radio, it is a little farther, because the atmosphere bends radio waves slightly downward. The radio horizon is therefore about 15 percent beyond the optical one in normal conditions.

The bending is expressed with an effective earth radius factor, usually written as k, with a typical value of about 4/3. Engineers calculate with an earth that is 4/3 as large as the real one, and the waves then travel in straight lines over it. This simple trick is the origin of the formulae that follow.

The horizon is not a hard limit. Signals continue past it, but they weaken quickly, because they are diffracted around the curve of the earth or scattered by the atmosphere. A good receiver can still hear a weak signal beyond the horizon, and special conditions such as ducting, described in our guide to tropospheric ducting, can extend the path to hundreds of kilometres.

The Formula

For a standard atmosphere, the radio horizon distance from one antenna is approximately:

• In kilometres: distance is 4.12 multiplied by the square root of the antenna height in metres.
• In miles: distance is 1.23 multiplied by the square root of the antenna height in feet.

For a link between two stations, add the horizon distances of both antennas. A station at 30 metres and a handheld at 2 metres therefore have a maximum line-of-sight path of about 4.12 times the sum of 5.48 and 1.41, which is roughly 28 kilometres. The square root has an important consequence. To double the range of one antenna, you must quadruple its height. That is why a modest increase from the roof edge to the top of a mast can change coverage noticeably, but going from a hilltop of 300 metres to 600 metres adds less than you might expect.

Range by Antenna Height

The table gives the radio horizon for a single antenna over smooth earth, using the standard 4/3 earth value. For a path between two antennas, add the two values. These are theoretical maxima, and obstacles reduce them.

The table shows why mountains and tall towers are the favourite sites for repeaters and for portable operation from a summit. It also shows how little a handheld can do at ground level: a link between two handhelds, each at 1.5 metres, has a theoretical limit of about 10 kilometres over flat ground, and it is usually far less in a town.

Three Worked Examples

Numbers make the formula easier to trust, so here are three common situations.

A handheld to a repeater. You stand in a field with the handheld at 1.5 metres. The repeater antenna is on a tower at 60 metres. The square root of 1.5 is 1.22 and the square root of 60 is 7.75, so the sum is 8.97, and multiplied by 4.12 gives about 37 kilometres. Over flat country, the link can be that long. In a town with buildings, the practical range may be a third of that, which is why a handheld that works in the field may be useless in a street.

Two mobile stations. Each has a magnetic-mount antenna at 2 metres on the roof of a car. The square root of 2 is 1.41, twice that is 2.83, and the result is about 11.7 kilometres. That is the usual range for simplex between two cars on open ground, and it matches what many operators see in practice.

A home station to a hill. You have a 12 metre mast and a friend operates from a hilltop at 250 metres. The square roots are 3.46 and 15.81, the sum is 19.27, and the horizon distance is about 79 kilometres. A modest station can therefore work a portable station on a summit that is far outside its own horizon, which explains why summit activations are so popular on VHF and UHF.

Weather and the Effective Earth

The factor of 4/3 is an average. When the air is cold near the ground and warm above it, the bending increases and the horizon moves farther away. When the air is unusually mixed, the bending decreases and the horizon shrinks a little. These changes are usually small, but they explain why a marginal link works on one morning and fails on another, and why VHF signals are often stronger in the early morning and on still, clear evenings. If you keep a log of signal strength from a distant repeater, you will see the pattern, and it is a good way to learn how local weather affects your paths. For anything that must work every day, leave a margin of several decibels above the minimum so that a poor day does not cut the link.

What Steals Range Before the Horizon

The horizon is the best case. In practice, several things reduce the distance.

Terrain and Buildings

A hill, a building or a belt of trees between the stations blocks or weakens the signal. At UHF, even a few trees or a wall cause significant loss, and a signal that is solid at VHF may be gone at 70 centimetres. Where the path is partly blocked, diffraction over the edge of an obstacle helps at lower frequencies, which is why 2 metres usually does better than 70 centimetres in difficult terrain.

The Fresnel Zone

The signal travels in an elliptical region around the straight line between the antennas, not only along the line itself. If an obstacle intrudes into the first Fresnel zone, the signal drops even though the direct line is clear. A rule of thumb is to keep about 60 percent of the first zone free of obstacles. For long links, this often means that the antenna must be higher than a simple line-of-sight sketch suggests.

Feed Line Loss

A tall mast is no help if the cable wastes half of the power. At 145 MHz and at 435 MHz, the loss of thin coax over 20 or 30 metres is large. Our guide to choosing coax for ham radio gives the numbers, and a low-loss cable can recover several decibels. A short, thick cable on a lower mast often beats a long, thin cable on a high one.

Polarization and Antenna Pattern

A vertical antenna on the transmit side and a horizontal one on the receive side lose a large part of the signal. Antenna patterns also matter, because a high-gain collinear squeezes its energy toward the horizon, which is useful for a repeater but not for a station on a hill that wants to reach a valley below.

Practical Ways to Extend Your Range

1. Raise the antenna. Height is the cheapest improvement, and mast sections, a chimney mount or a place on a hill all help. Follow the safety advice in our article on push-up masts and guying.
2. Use low-loss cable. Replace thin coax with a better type and keep the run short.
3. Use a better antenna. A Yagi or a collinear adds gain in the direction you need, and the effect is like adding transmitter power, but without the cost.
4. Match the polarization. Use vertical for FM and repeaters and horizontal for weak-signal SSB and CW.
5. Add a preamplifier at the antenna for receive-only improvement, as described in our guide to mast-mounted preamplifiers, if your receiver is limited by cable loss.
6. Choose a better location. A short walk to the top of a hill or the edge of a building can open a path that was blocked before.

Using the Horizon in Your Planning

The horizon helps in several practical situations. When you plan a portable operation, choose a summit or a clear ridge with a view toward the stations that you want to work, and estimate the range with the table. When you set up a link or a simplex net, decide who needs to be on a high point and who can stay below. When you look for a repeater, check whether its tower height and your location give a clear line, and if not, aim a directional antenna at the repeater instead of using an omnidirectional one. For event work, such as a marathon or a field day, a few high-placed stations can relay for the rest, which reduces the need for expensive equipment. Finally, when you test a new antenna, do it on a day with normal conditions and compare to an earlier reference, so that a temporary lift does not mislead you.

Basic operating practice is covered in our article on VHF and UHF simplex and repeater operating, and the horizon explains most of the situations that it describes.

When Signals Go Beyond the Horizon

Sometimes the calculation fails in your favour. A temperature inversion near the ground can create a duct and carry signals for hundreds of kilometres. Meteor trails reflect VHF signals briefly, and a sporadic E layer can give VHF contacts over thousands of kilometres. Mountain ridges can scatter weak signals in the knife-edge effect. None of these is reliable, and a link that you depend on should work under normal conditions. Use the horizon figures for design and treat everything beyond them as a bonus.

Common Mistakes

• Spending on power instead of height. A higher antenna usually beats a stronger amplifier on VHF and UHF.
• Ignoring cable loss. A long run of thin coax can waste most of the gain of a tall mast.
• Forgetting the second station. The range depends on both ends, so a low handheld limits a link with a high repeater.
• Assuming flat ground. Hills, buildings and trees block the path long before the geometric horizon.
• Treating a duct as normal. Unusual openings are fun, but they cannot support a reliable link.

The Bottom Line

The radio horizon explains most of what you see on VHF and UHF. The distance in kilometres is about 4.12 times the square root of the antenna height in metres for each end, and you add the two. Height beats power, thick cable beats thin cable, and a clear Fresnel zone beats a clear line drawn on a map. Estimate the range with the table, raise the antenna where you can, choose a good spot, and keep unusual propagation for the days when it appears.

Frequently Asked Questions

What is the radio horizon?

It is the distance at which two antennas lose line of sight because of the curve of the earth, extended slightly because the atmosphere bends radio waves downward.

How do I calculate the radio horizon?

Use 4.12 times the square root of the antenna height in metres to get kilometres, or 1.23 times the square root of the height in feet to get miles. Add the values for both stations.

Why is VHF and UHF range limited?

Signals at these frequencies are not reflected by the ionosphere in normal conditions, so they travel along line of sight and are blocked by the curve of the earth and by obstacles.

Does more power increase the radio horizon?

No. Power can help a weak signal be heard, but the horizon depends on antenna height and terrain, and beyond it the signal falls quickly.

Why does 2 metres go farther than 70 centimetres in hilly terrain?

Lower frequencies diffract better over edges and pass through trees and walls with less loss, so they often fill gaps that block higher frequencies.

Can I work beyond the horizon?

Sometimes. Ducting, sporadic E, meteor scatter and diffraction extend the path on some days, but they are not reliable for everyday links.