Clearing the Fresnel zone

Author: Claude Opus 5.5 (LLM), published by Leonardo Pinero-Perez
Written: 8 Nov 2026
Updated: 8 Nov 2026
Review: Not reviewed for accuracy
Topic: Radio

A point-to-point radio link needs more than a straight line between two antennas. It needs a clear, football-shaped volume around that line, and the size of that volume depends on frequency and distance.

Line of sight is not enough

Two antennas can see each other and the link can still underperform. Radio energy does not travel along a single ray; it spreads through a region around the direct path. Obstacles inside that region, like a ridge crest, trees or a roof, reflect and diffract part of the signal, which then arrives out of phase with the direct wave and partly cancels it.Note 1Named after Augustin-Jean Fresnel, who worked out the zone construction for light in his studies of diffraction.

These regions are the Fresnel zones: ellipsoids with the two antennas at their foci. The first zone holds the points where a bounced path is at most half a wavelength longer than the direct one. It carries most of the energy, so it is the zone link planners care about.

How wide it is

At a point d₁ km from one end and d₂ km from the other, on a link D km long at f GHz, the radius of the first zone in metres is 17.32 √(d₁d₂ / fD). It is widest at the midpoint and shrinks to nothing at each antenna. Higher frequencies give a thinner zone, which is one reason millimetre-wave links can thread gaps that a 2.4 GHz link cannot.

Figure 1The first Fresnel zone on a 10 km link at 5.8 GHz, with a radius of 11.4 m at the midpoint. The ridge enters the zone but stays out of the inner 60 percent (dashed). Vertical scale exaggerated.

First-zone radius at the midpoint of a 10 km link
Frequency	Radius (m)	60% clearance (m)
2.4 GHz	17.7	10.6
5.8 GHz	11.4	6.8
11 GHz	8.3	5.0
24 GHz	5.6	3.4
60 GHz	3.5	2.1

The 60 percent rule

Planners usually keep at least 60 percent of the first zone’s radius clear of obstacles.Note 2With about 60 percent of the first zone clear, the path loses roughly what it would in free space. The exact figure depends on the shape of the obstruction. On longer links the earth itself gets in the way: the ground bulges up between the two ends by about d₁d₂ / (12.74 k) metres, where k is the effective earth-radius factor, usually taken as 4/3.Note 3k accounts for the atmosphere bending radio waves slightly back toward the ground. 4/3 is the standard-atmosphere value; planners also check lower values for days when the bending is weaker. At the midpoint of a 10 km path that is about 1.5 m.

A quick check in code

import math

def fresnel_radius_m(d1_km, d2_km, f_ghz):
    """First Fresnel zone radius, metres."""
    d_km = d1_km + d2_km
    return 17.32 * math.sqrt(d1_km * d2_km / (f_ghz * d_km))

r = fresnel_radius_m(5, 5, 5.8)   # 11.4 m
print(f"keep {0.6 * r:.1f} m clear")  # keep 6.8 m clear

The numbers above matter less than the picture they add up to.

The purpose of computing is insight, not numbers.

Richard Hamming, Numerical Methods for Scientists and Engineers, 1962

Spotted an error, or want to reply? Email me: leonardo.pinero42 [at] gmail [dot] com