Fresnel Zone Calculator
Calculate first Fresnel zone radius and the clearance a wireless link needs at any point along the path, including earth curvature.
Result
Clearance profile along the path
| Position from A | Fresnel radius | 60% clearance | Curvature bulge |
|---|---|---|---|
| 1 km | 7.01 m | 4.2 m | 0.71 m |
| 2.5 km | 10.11 m | 6.07 m | 1.47 m |
| 5 km | 11.68 m | 7.01 m | 1.96 m |
| 7.5 km | 10.11 m | 6.07 m | 1.47 m |
| 9 km | 7.01 m | 4.2 m | 0.71 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
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.