Calculate radar line-of-sight horizon distance from antenna and target heights. Includes atmospheric refraction (k-factor), Fresnel zone, and target height lookup table.
The radar (or radio) horizon is the maximum distance at which a radar or radio signal can propagate in a straight line from an antenna to a target, limited by the curvature of the Earth. For standard atmospheric conditions, the refraction factor k = 4/3 extends the horizon about 15% beyond the geometric (optical) horizon.
This calculator computes the radar horizon distance from antenna height and target height, accounting for atmospheric refraction via the adjustable k-factor. It also calculates the geometric horizon (k=1) for comparison, the wavelength at the given frequency, and the first Fresnel zone radius at the horizon.
A target height table shows the maximum line-of-sight range for surface, 10m, 100m, 1km, and 10km target heights — essential for understanding detection envelopes. The refraction conditions table explains sub-refraction, standard, super-refraction, and ducting.
This tool is used by radar engineers, RF link designers, maritime navigators, and ATC planners to determine coverage limits.
Use this calculator when antenna height, target height, and atmospheric conditions all affect the usable line of sight. It is handy for radar coverage checks, microwave link planning, and marine or aviation visibility estimates.
The target-height table helps compare surface targets with elevated targets under the same refraction setting, which makes it easier to judge whether the horizon is limiting the link.
d = √(2·k·Re·h_a) + √(2·k·Re·h_t). where Re = 6,371 km, k = 4/3 standard. Geometric (no refraction): k = 1. Simplified: d(km) ≈ 4.12·(√h_a + √h_t) for k=4/3, h in meters.
Result: Radar horizon = 18.4 km (9.9 NM)
d = √(2 × 4/3 × 6371000 × 20) = √(339.8×10⁶) = 18,400 m = 18.4 km. With k=1: d = 16.0 km. Refraction adds 15%.
The k-factor changes the effective Earth radius used in the horizon calculation. A higher value means the atmosphere bends radio waves more strongly downward, which extends the horizon.
For marine radar, use the height of the antenna above the waterline. For land-based links, compare both antenna heights and watch for terrain that may block the first Fresnel zone.
- k = 1: geometric horizon with no refraction - k = 4/3: standard radio atmosphere - k > 4/3: super-refraction or ducting conditions - k < 1: sub-refraction, which shortens the range
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The k-factor accounts for atmospheric refraction bending radio waves downward. k = 4/3 (1.333) is the standard for temperate climates. k varies from ~0.7 (extreme sub-refraction) to infinity (ducting).
Super-refraction (k > 4/3) happens when warm, dry air overlies cool, moist air — common over warm ocean surfaces. It extends radar range beyond normal but can create blind zones.
Ducting occurs when the atmospheric refractive index decreases so rapidly with height that radio waves are trapped in a layer, bending downward more than the Earth curves. This can extend radar range by hundreds of km — or create complete detection failures at certain altitudes.
The horizon distance is independent of frequency. However, frequency affects diffraction around the horizon, atmospheric absorption, and the Fresnel zone clearance required for practical link design.
Radio and optical horizons use the same geometry but different k-factors. For optics, k ≈ 1.06-1.08 (visible light refracts less than microwaves). For radio: k ≈ 4/3.
This calculator assumes a smooth, spherical Earth. Terrain obstructions (hills, buildings) reduce the effective line of sight. For real link planning, use terrain profile tools with digital elevation models.