Radio Horizon & Line-of-Sight Distance Calculator
Maximum line-of-sight distance between two antennas from their heights — optical horizon and the 4/3-earth radio horizon, the height needed to reach a given distance, and the bulge of the Earth in the middle of the path.
How it works
Radio horizon d (km) = 4.12 √h (m) per antenna (k = 4/3 effective Earth radius; optical 3.57 √h); total LOS = d₁ + d₂; Earth bulge (m) = d² ÷ (8 × 8,495 km) × 1,000
VHF, UHF and microwave signals travel essentially in straight lines, so the curve of the Earth sets a hard limit on how far two antennas can see each other. Because the lower atmosphere is denser near the ground, radio waves refract slightly downward and the effective Earth looks about a third larger than it is — the “4/3 Earth” — so the radio horizon is about 15% beyond the optical one. Each antenna’s horizon scales with the square root of its height: doubling height gains only 41% in distance, which is why tall towers and hilltop sites matter more than transmitter power. For a real link the straight line must also clear terrain and buildings, plus most of the first Fresnel zone; Earth bulge at mid-path shows how much a flat-looking path actually rises. HF and some VHF conditions (tropospheric ducting, sporadic-E) can carry signals far beyond this, but they cannot be planned on.
Worked example
Antennas at 30 m and 10 m see 22.6 km and 13.0 km to their horizons — 35.6 km of radio line of sight (30.8 km optical). A 40 km path is 4.4 km too far; raising antenna 2 to about 17.9 m closes it. Mid-path the Earth bulges 23.5 m, so a 20 m building halfway would block it.
Frequently asked questions
Does this apply to HF (shortwave)?
No — HF reaches around the world by refracting off the ionosphere. Line-of-sight limits apply above about 30 MHz, and even there tropospheric ducting occasionally extends range several times.
Why does the Wi-Fi/LoRa manual quote longer ranges?
Those assume ideal line of sight, often from elevated sites; with both ends near the ground the horizon, not the radio, is the limit — a 2 m node sees only 5.8 km.
Related calculators
Free-space / textbook estimate. Terrain, buildings, foliage, rain and multipath change real links substantially; licensed services must follow their regulator’s limits.