VHF and UHF Range Calculator: Radio Horizon by Antenna Height

Above 50 MHz, range is a geometry problem before it is a radio problem. Signals travel in something very close to straight lines, the earth curves away underneath them, and the single largest lever anyone has over how far they reach is how high the antenna is. Power helps with obstacles. It does nothing at all about the horizon.

Where the formula comes from

Geometry gives the distance to the visual horizon as 1.22 times the square root of height in feet, in miles. Radio does better than light because the atmosphere is denser near the ground, which bends signals slightly downward and effectively increases the earth's radius by about a third. Applying that four-thirds earth correction gives 1.415 times the square root of height, which is the figure used everywhere in VHF and UHF planning.

The square root is the important part. Doubling height does not double range; it multiplies it by the square root of two, about 1.41. Quadrupling height doubles range. This is why the step from a handheld at head height to an antenna on a rooftop is transformative and the step from a 30 foot mast to a 40 foot mast is not.

Why the repeater does all the work

Two handhelds at head height each have a horizon of about 3.5 miles, so their combined theoretical range is about seven miles and their real suburban range is one to two. Put a repeater on a 1000 foot hill and its horizon alone is nearly 45 miles, so a handheld five miles from the repeater reaches it, and so does another handheld forty miles the other side. Two stations that cannot hear each other at all can hold a conversation through it.

That is the entire function of a repeater and it explains most of what new operators find confusing about VHF. The repeater is not amplifying your signal in any useful sense; it is lending you its height. Everything else about repeaters, the offsets and the tones, is administrative detail on top of that one idea, and it is covered on how to use a repeater.

Why power barely helps

Going from a 5 watt handheld to a 50 watt mobile is 10 decibels, which is a genuinely large improvement and it buys you exactly one thing: margin. Margin punches through foliage, through building walls, and through the partial obstruction of a low ridge. It does not move the horizon at all, because the horizon is set by geometry rather than by signal strength.

The ordering to take from that table: antenna first, height second, power last. A Nagoya NA-771C 15-inch whip$15.98 costs sixteen dollars and improves receive as well as transmit, which no amount of transmit power does. A Diamond X50A dual-band base antenna$122.99 on a mast changes both gain and horizon at once, and it is the single largest improvement available to a VHF station.

Feedline: the loss that undoes the height

Getting an antenna to 30 feet and feeding it with the wrong cable can give away everything the height bought. A hundred feet of RG-58 at 146 MHz loses about 5 decibels, which is more than two thirds of your power and an equal penalty on receive. The same run in LMR-400 class cable loses about 1.5.

That is a bigger difference than the step from 5 watts to 25, and it applies in both directions, which transmit power does not. On any VHF or UHF run longer than about twenty-five feet, buy Bolton400 low-loss coax, 100 ft with PL-259$119.95 and stop thinking about it. The arithmetic for your own run is on the coax loss calculator.

When VHF goes much further than this page says

• Tropospheric ducting. A temperature inversion, common over water and on calm nights, traps signals in a layer that behaves like a waveguide. Two metre contacts of several hundred miles happen this way and can last for days.
• Sporadic E. Intense patches of ionisation in the E layer reflect signals up to about 150 MHz over distances around 800 to 1400 miles. This is why 6 metres is called the magic band; it opens without warning and closes just as fast.
• Aircraft scatter. A signal bounced off an airliner, usable for the few minutes the geometry lines up. Predictable enough that weak-signal operators plan around flight paths.
• Meteor scatter. Ionised trails from meteors reflect VHF signals for fractions of a second to several seconds. Digital modes designed for very short bursts make this a routine mode rather than a curiosity.
• Earth-Moon-Earth. Bouncing a signal off the moon. It works, it needs large antennas and careful receivers, and it is one of the reasons the Amateur Extra pool covers it.

None of these is reliable and none should be assumed when planning emergency communications. They are what makes VHF interesting rather than what makes it work.

Getting your own antenna higher

The horizon table makes the case: moving from a handheld held at head height to a vertical at 30 feet takes your horizon from 3.5 to 7.7 miles and adds several decibels of antenna gain on top. That is a larger change than any radio upgrade at any price.

• A roof tripod such as a Skywalker heavy duty roof tripod with mast$60.99 gets a vertical above the roofline. Flashing and sealing the lag bolts is the entire job.
• A fascia J-mount such as a Skywalker J-pipe antenna mount, 38 in$49.99 is the option that puts no holes through the roof deck.
• A push-up mast such as an Easy Up 20 ft telescoping push-up mast$185.00 reaches 20 feet and must be guyed at full extension with a Threlaco 3-way galvanized guy wire kit, 50 ft$46.99.
• The antenna itself. A Diamond X50A dual-band base antenna$122.99 is the default dual-band rooftop vertical. A Tram 1465 NMO to UHF ground plane kit$37.99 turns an existing NMO mobile whip into a base antenna with ground-plane radials for a fraction of the price.

Before choosing where any of it goes, walk the site and find every overhead conductor including your own service drop. Contact with a power line during the raising is the most common fatal accident in amateur radio, and no amount of range is worth being anywhere near one. Full treatment on antenna and mast installation safety.