Fresnel Zone Calculator

All three use the same formula r = sqrt(n × wavelength × d1 × d2 / D), differing only in the zone number n (1, 2, or 3) multiplied inside the square root. Because it's inside a square root, the radius grows with sqrt(n) rather than linearly — the 2nd zone is about 1.41× the 1st zone's radius and the 3rd is about 1.73×, not simply double or triple.

The d1 × d2 product in the Fresnel radius formula is maximized when the obstacle sits exactly at the path midpoint (d1 = d2 = D/2), which is also where fresnelMax is computed directly as sqrt(wavelength × D / 4). Obstacles closer to either antenna produce a smaller Fresnel radius at that point, so the midpoint is the worst case for clearance planning and the sensible default to check first.

It's the extra apparent height an obstacle gains partway along a long path purely because the Earth's surface curves away from a straight line between the antennas, computed as (d1 × d2) / (2 × Earth radius × 1.333). The 1.333 factor (4/3-Earth-radius approximation) doesn't come from the planet's actual curvature alone — it also accounts for how the atmosphere's refractive gradient bends radio waves slightly downward, effectively making the usable radio horizon appear as if Earth were about a third larger than it really is.

Signal energy contributing to constructive interference is concentrated toward the center of the first Fresnel zone, and empirical link-planning experience shows that keeping the inner 60% of that radius free of obstructions preserves signal strength close to true free-space conditions. That's why the calculator reports clearance60 as a highlighted output alongside the full fresnel1 radius — it's the practical design threshold, not the theoretical zone boundary itself.