Formula and Method for the Radar Horizon
The radar horizon is the maximum line-of-sight distance at which a radar antenna and a target can theoretically detect each other over the curve of the Earth, based on each one's height above the surface. Because the Earth is round, both the radar and the target are limited by their own local horizons — and because the lower atmosphere is denser than the air above it, radio waves bend (refract) slightly toward the ground as they travel, letting radar "see" roughly 15% farther than a purely geometric (optical) horizon would allow. This calculator uses the standard effective-Earth-radius model, d = √(2·k·R·h), to find the horizon distance contributed by each height, then adds the two together for the maximum unobstructed detection range.
How the calculation works
For an antenna or target at height h above a sphere of effective radius k·R — where R ≈ 6,371 km is Earth's mean radius and k is the refraction factor — the distance to that object's own horizon is d = √(2·k·R·h). A standard atmosphere refracts radio waves enough that k = 4/3 ≈ 1.333 is the conventional default; k = 1 gives the purely geometric (optical) horizon with no refraction. Because a radar can detect a target only once the target rises above both horizons, the maximum radar-to-target range is the sum of the two individual horizon distances: d(total) = √(2kRh₁) + √(2kRh₂), where h₁ is the antenna height and h₂ is the target height. This calculator converts your inputs to meters, applies that formula, and reports the total in your chosen distance unit plus nautical miles, the standard unit in aviation and maritime radar work.
Common mistakes
- Using only the antenna height: a low radar can still detect a high-flying target far beyond its own horizon, because the target's altitude contributes its own horizon distance — always add both terms.
- Assuming k = 1 by default: a standard atmosphere already bends radar waves, so k = 4/3 is the normal working value; using k = 1 without reason understates real-world range.
- Treating the radar horizon as the detection range: the radar horizon is a geometry and propagation limit only. Actual detection also depends on the radar equation (transmit power, antenna gain, target radar cross-section, receiver sensitivity) and on terrain blocking the path — the real maximum range is the smaller of the radar horizon and the radar-equation range.
- Mixing height units: enter both the antenna height and target height in the same unit (meters or feet); the calculator will not convert them for you if they are inconsistent.
Real-world applications
- Air traffic control and air-defense radar siting, where antenna tower height and cruising altitude both determine coverage radius.
- Maritime radar range planning for ship-to-ship and ship-to-coast detection, where antenna mast height sets the base horizon.
- VHF/UHF and microwave communication link planning, which uses the same curvature-and-refraction horizon formula for line-of-sight radio links.
- Estimating the minimum antenna or tower height needed to cover a target area or altitude band.