Radar Horizon Calculator

Radar horizon is the maximum distance at which a target can still be detected by radar before Earth's curvature hides it. It is purely a geometric limit, not a transmitter power limit: the higher the radar antenna and the higher the target, the farther the horizon.

d = sqrt(2 x R x h), with h the antenna height in meters and R Earth's radius in meters. For radio waves the effective 4/3 radius is used (R = 8,495,000 m), so d(km) is roughly 4.12 x sqrt(h[m]). Without refraction correction (R = 6,371,000 m), the formula becomes d(km) roughly 3.57 x sqrt(h[m]).

The atmosphere bends radio waves slightly downward, so practical radio range is farther than pure geometric line of sight. The standard telecommunications model replaces Earth's radius with 4/3 x 6,371 km = 8,495 km so that one simple formula stays accurate under normal atmospheric conditions.

With the 4/3 model: d = sqrt(2 x 8,495,000 x 30) = 22,576.5 meters = 22.5765 km (12.1904 nautical miles). Without refraction: 19.5515 km. This value is verified against high-precision calculation in this calculator.

Sum each side's horizon: d_total = d1 + d2. Verified example: a 30 m radar and a 10 m target give 22.5765 + 13.0346 = 35.6111 km with the 4/3 model.

There is no formula difference: both use the effective 4/3 radius model for radio waves. The term radar horizon is common in detection, defense, and maritime contexts, while radio horizon is used in telecommunications and amateur radio.

Visual horizon uses visible-light bending with a practical factor of about 3.86 x sqrt(h), while radar and radio horizon use the 4/3 model for radio waves (about 4.12 x sqrt(h)). For eyes, lighthouses, or photography, use the visual horizon distance calculator in the Related Tools link.

The first Fresnel zone is the ellipsoid region around the line of sight where most wave energy travels, with radius r = sqrt(lambda x d1 x d2 / D). Standard practice requires at least 60 percent of the first zone to be obstacle-free so the signal does not weaken significantly. Example: a 10 km link at 2.4 GHz has a 17.67 m radius at the midpoint, requiring 10.60 m of clearance.

The nautical mile is the standard unit of maritime and aviation navigation, the two main users of radar horizon calculations. One nautical mile equals 1,852 meters.

The formula assumes Earth is a perfect sphere with a standard atmosphere. Phenomena such as atmospheric ducting, heavy rain, or uneven terrain can change field results. Use it as a planning estimate, not a replacement for a professional RF survey.