Radar Horizon Calculator

The radar horizon is the approximate maximum line-of-sight distance between a radar antenna and a target when Earth's curvature blocks the direct path. Raising either endpoint extends the horizon because the line from that endpoint can remain clear of the curved surface for a longer distance. This calculator adds the horizon distance from the antenna to the tangent point and the corresponding distance from the target to its tangent point. Heights are measured in meters above the relevant local surface, and results are shown in kilometers and nautical miles. A purely geometric calculation uses Earth's mean radius and assumes rays travel in straight lines. In the lower atmosphere, refractive-index gradients commonly bend radio and radar energy slightly toward Earth. Engineers often model this behavior by multiplying Earth radius by an effective-radius factor called k. A conventional standard-atmosphere assumption is four-thirds, entered here as approximately 1.333333. That value extends the predicted radio horizon beyond the optical geometric horizon. Setting k to one removes the refraction adjustment. Real propagation can depart substantially from the standard model. Temperature inversions, humidity gradients, weather fronts, terrain, sea state, clutter, diffraction, and atmospheric ducting can change detection conditions. Super-refraction or ducting may carry energy much farther than a simple horizon estimate, while sub-refraction may shorten the useful path. The target's radar cross section, transmitter power, antenna pattern, receiver sensitivity, frequency, interference, and required probability of detection also determine whether a target is actually observed. Treat the horizon as a curvature-limited line-of-sight boundary, not a guaranteed instrument range. Use height above the local reflecting or obstructing surface rather than elevation above an unrelated datum. For preliminary siting, this calculation can compare antenna towers, target heights, and assumed refractivity. Operational system design should incorporate terrain profiles, propagation models, link budgets, radar performance equations, measured refractivity, and suitable engineering margins. Safety-critical aviation, maritime, and defense decisions require validated data and approved procedures rather than this simplified estimate.