Fresnel Zone Calculator

Calculate first Fresnel zone radius and the clearance a wireless link needs at any point along the path, including earth curvature.

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Result

First Fresnel zone radius
11.68 m
Required 60% clearance
7.01 m
Earth curvature bulge
1.96 m
k = 4/3 refraction
Total clearance needed
8.97 m
above the obstacle at this point
Obstacle at
5 km from A, 5 km from B

Clearance profile along the path

Position from AFresnel radius60% clearanceCurvature bulge
1 km7.01 m4.2 m0.71 m
2.5 km10.11 m6.07 m1.47 m
5 km11.68 m7.01 m1.96 m
7.5 km10.11 m6.07 m1.47 m
9 km7.01 m4.2 m0.71 m

The maths

Fresnel radius formula
r = 17.32 × √(d1·d2 / (D · f_GHz)) [metres, km, GHz]
Earth bulge formula
h = d1·d2 / 12.75 (k = 4/3)
Design rule
keep at least 60% of the first zone clear
Where obstructions hurt
The zone is widest at mid-path, so a tree exactly halfway is far more damaging than the same tree near either end. Clearance requirements also grow with distance and shrink with frequency - a 30 km 2.4 GHz link needs far more headroom than a 2 km 5.8 GHz one.

About Fresnel Zone Calculator

Radio does not travel in a pencil-thin line. It occupies an ellipsoid around the direct path, and obstructions inside that volume cause diffraction loss even with perfect visual line of sight. The convention is to keep at least 60% of the first Fresnel zone clear.

Refraction and the k-factor

Radio bends slightly toward the earth because atmospheric density falls with height, which effectively flattens the earth for planning purposes. The standard assumption, k = 4/3, is what the bulge formula here uses. Under temperature inversions k varies, and on long paths over water it can drop below 1, raising the effective obstruction and turning a marginal link into a failing one for hours at a time. Long overwater hops are designed with extra clearance for exactly this reason.

Why visual line of sight is not enough

You can see the far antenna over a hedge and still lose 6-10 dB to diffraction, because the hedge intrudes into the zone. Conversely, an obstruction blocking under 40% of the first zone typically costs very little. Add earth curvature on longer paths: at 30 km the mid-path bulge is around 17 m before any terrain is considered.

Common use cases

  • Sizing tower or mast height for a planned hop.
  • Deciding whether a tree line will actually matter.
  • Explaining a link that degrades as vegetation grows through the season.

Edge cases and gotchas

  • Trees grow. Design for the canopy in ten years, not today.
  • Over water, reflections create multipath fading that clearance alone does not solve - consider antenna height diversity.

Frequently asked questions

What if I only have 40% clearance?
Expect a few dB of diffraction loss - often survivable with a good fade margin, but it is the first thing to blame when the link degrades in bad weather.
Does the zone matter at short range?
Less: at 500 m and 5 GHz the radius is under 2 m. Clearance problems scale with path length, which is why long low-frequency hops are the hard ones.