How this calculator works
For heights much smaller than Earth radius, the horizon distance is approximately sqrt(2Rh). The two endpoint horizons add. Standard radio refraction is represented by replacing R with 4R/3, which increases range by about 15.5%. Height inverses return the minimum non-negative height to meet or exceed the requested range. This is a line-of-sight geometry estimate, not a detection guarantee or a ducting prediction.
Formula
d = sqrt(2kRh1) + sqrt(2kRh2), with k = 1 or 4/3. Required h1 = max[0, d-sqrt(2kRh2)]²/(2kR).
Worked example
With a 500 m model radius and heights of 1 m and 4 m, the geometric approximation gives 94.8683 m. Real Earth radii and low antenna heights give distances in kilometres.
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Frequently asked questions
Does standard refraction always apply?
No. Temperature and humidity profiles can increase, reduce or duct propagation.
Why are the two horizons added?
The endpoints can see each other when their horizon paths meet.
Does a target within range always appear on radar?
Detection also depends on radar cross-section, frequency, clutter, power, receiver performance and terrain.