Radio Horizon Calculator
Antenna heights to horizon and link miles.
What it does
Radio waves fly straight while Earth curves away, so antenna height sets talking distance more than watts do. The radio horizon stretches about 1.23 times the square root of feet. Two stations add horizons.
The tool above takes one or two antenna heights and prints horizon miles plus combined link range over smooth earth. Thirty feet sees 6.7 miles; paired with a ten-foot mast the link spans 10.6.
Amateur-radio references with communications regulator guidance teach this same root-height form for VHF and UHF planning. Height dominates because roots grow slowly; doubling height adds about forty percent, never double.
Treat answers as ceilings for flat open paths. Hills, forests, buildings, and ducting all rewrite reality, so raise metal, clear zones, and confirm every critical link on site.
How to use
- Enter primary antenna height in feet.
- Enter second height, or 0.
- Read horizon miles.
- Read combined link miles.
- Site-test before trusting links.
- Raise height to reach further.
Formula
- h1
- First antenna height in feet.
- h2
- Second antenna height, 0 for horizon only.
Smooth-earth optical horizon with standard refraction folded into 1.23. Heights run feet; second height 0 means one-way horizon. Obstructions always shorten reality.
Worked example
Example: 30 ft plus 10 ft
30 ft shore antenna to 10 ft boat antenna.
- Antenna stands 30 ft over flat ground.
- Horizon: 1.23 x root(30) = 6.7 mi.
- Boat antenna adds 10 ft: 1.23 x root(10) = 3.9.
- Link spans 6.7 + 3.9 = 10.6 mi.
- Hills, trees, and buildings shrink it.
Reference table
| Height | Horizon | With 10 ft far end |
|---|---|---|
| 10 ft | 3.9 mi | 7.8 mi |
| 30 ft | 6.7 mi | 10.6 mi |
| 50 ft | 8.7 mi | 12.6 mi |
| 100 ft | 12.3 mi | 16.2 mi |
Limits
- Smooth earth only. Terrain always shortens.
- VHF/UHF planning; HF skips past it.
- Refraction folded in, not weather live.
- Site tests sign real links.
Common mistakes
- Counting watts instead of feet.
- Forgetting the far-end height.
- Trusting smooth-earth math in hills.
- Planning HF by horizon rules.
- Skipping field tests.
Try it yourself
Quick checks. Answers sit tucked under each question.
Horizon from a 50 ft tower?
Horizon is 1.23 x root(50) = 8.7 mi with no far end.
Horizon from a 100 ft tower?
Horizon is 1.23 x root(100) = 12.3 mi with no far end.
Questions
How far does an antenna see?
About 1.23 times the square root of height in feet, in miles. Thirty feet sees 6.7 miles; one hundred sees 12.3. Two stations add horizons together.
What does the math assume?
Smooth-earth line of sight without refraction extras. Real paths lose to hills, trees, buildings, and curvature quirks; treat answers as ceilings.
Do two antennas double it?
Yes: add both horizons for station-to-station range. Two 30-foot antennas span about 13.5 miles over flat ground.
Height or power: which reaches further?
Height dominates: doubling height stretches range about 41 %, since roots grow slowly. Fifteen extra feet on a short mast beats five on a tall one.
Does this cover HF radio?
VHF and UHF hug line of sight; HF bounces skywave past it. This page serves VHF/UHF planning; HF needs propagation tools instead.
How do I extend real range?
Raise the antenna, clear the Fresnel zone, and test on site. Models plan links; field checks sign them.