Radar Horizon Calculator

Radio waves bend slightly around the Earth, so the radar horizon is farther than the optical one.

How the Math Works

The radar horizon calculator uses the formula d ≈ 4.12·√h, where d represents the maximum line-of-sight distance in kilometres and h is the antenna height in metres. This relationship stems from geometric considerations: the Earth's curvature limits how far a radar signal can travel before it dips below the horizon. The constant 4.12 incorporates the Earth's radius and accounts for standard atmospheric refraction, which bends radio waves slightly downward, extending the theoretical horizon by approximately 15% compared to pure geometric calculations. Taking the square root of the height reflects the inverse relationship between antenna elevation and the distance-to-height ratio in spherical geometry.

Practical Applications

To use this calculator, simply enter your radar or antenna height in metres and multiply by 4.12 after taking the square root of the height. For example, a radar station on a 100-metre tower would have a horizon distance of 4.12·√100 = 4.12·10 = 41.2 kilometres. This calculation is essential for determining the maximum detection range of surveillance radars, planning radio communication links, and establishing the operational coverage area of radio telescopes or weather stations. Engineers use this to size radar networks and optimize antenna placement for complete area coverage.

Day-to-Day Use

While most people don't calculate radar horizons daily, this principle affects technologies we use regularly. Your smartphone's GPS accuracy, aircraft collision avoidance systems, and even satellite TV dish placement all rely on line-of-sight calculations similar to radar horizon. Understanding this concept helps explain why radio and TV signals sometimes disappear when you move to a different location, why cell towers need to be strategically placed, and how weather balloons and drones communicate with ground stations. It also illuminates why tall buildings and mountains can block wireless signals, affecting everything from Wi-Fi coverage to emergency broadcast reception.

Worked example

30 m antenna → about 22.6 km.

FAQ