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Fresnel Zone Calculator: First-Zone Radius, 60% Clearance and Earth Bulge

Enter frequency, path length and obstruction position to get the first Fresnel zone radius, the 60% clearance you should design for, and the earth-curvature bulge you have to add on long paths. Works for any point-to-point link from 100 MHz to 40 GHz.

Metric results, imperial shown too k-factor adjustable for water paths Live recalculation, no sign-up

Link inputs

Change any value and the results update immediately.

MHz
2,400 MHz = 2.4 GHz. Common values: 433, 868, 915, 2400, 3500, 5800.
km
%
Distance from antenna A. 50% checks mid-path, where the zone is widest.
m
Fill this to get the minimum antenna height at the obstruction.

Band presets

One click sets the frequency field.

First Fresnel zone radius at the obstruction
12.5m
= 41.0 ft
Distance from antenna A to obstruction (d1)2.50 km
Distance from obstruction to antenna B (d2)2.50 km
First zone radius at mid-path12.5 m
60% clearance to keep free (radius)7.50 m
Earth bulge at that point0.37 m
Obstacle + 60% clearance (above obstacle top)7.87 m
Minimum antenna height above ground—
Checked at mid-path, where the zone is widest. Any other point on a flat route has more clearance.

Radius uses path length and frequency only. The earth bulge term is what changes with k; it is added once, on top of the 60% clearance.

How this is calculated

r1 = 17.32 × √( d1 × d2 / ( f × D ) )
  r1 in metres  |  d1, d2, D in km  |  f in GHz

mid-path: r1 = 8.657 × √( D / f )

earth bulge: h = d1 × d2 / ( 2 × k × 6371 ) × 1000

The 17.32 constant already contains the 300 m/µs speed of light and the kilometre-to-metre conversion, which is why frequency is entered in GHz and distance in km. At mid-path the two branches are equal, so the equation collapses to the familiar 8.657 form.

What the Fresnel zone actually is

The first Fresnel zone is the ellipsoid of space around the straight line between two antennas. It is widest at the middle of the path and narrows to a point at each antenna. Radio energy that travels slightly off the direct line still reaches the receiver, and up to a point it arrives in phase and adds to the main signal. Block that volume and you lose the contribution — the link still works, but with less margin and more sensitivity to fading.

Antenna A Antenna B obstruction 60% clearance first Fresnel zone (r₁) ground

The dashed ellipse is the first zone; the red volume is what has to stay free. Roughly 60% of the radius is the practical design target.

Why 60% and not 100%

Keeping the full zone clear is not achievable on most real routes, and it is not necessary. Obstruction loss stays close to zero until the intrusion reaches about 40–50% of the radius, then rises steeply. Designing for 60% clear gives a working margin without demanding a taller mast than the terrain allows.

Why the earth bulge term exists

Radio paths are drawn straight, but the earth curves away underneath them. Over a 5 km path that is about 37 cm at mid-point; over 30 km it is more than 13 m, and it works against you exactly where the zone is widest. The k-factor describes how much the atmosphere bends the beam: k = 4/3 is the standard temperate-land value, while paths over water or hot coastal ground can drop toward k = 2/3, which increases the bulge and eats clearance.

Worked example: 5.8 GHz over 8 km

StepValueNote
First zone radius at mid-path10.2 m8.657 × √(8 / 5.8)
60% clearance target6.1 m0.6 × 10.2 m, above the obstacle top
Earth bulge at mid-path, k = 4/30.94 m4 × 4 / (2 × 1.333 × 6371) × 1000
Total clearance to plan for7.0 m6.1 m + 0.94 m
Same path, k = 2/38.0 mbulge rises to 1.88 m

That last row is the reason coastal links get into trouble: the antenna height that worked in a winter survey is short by almost a metre in summer, when the k-factor drops.

Clearance is necessary, not sufficient. A path with 60% clearance can still fail on rain fade, multipath over water, or interference. Use the link budget calculator to check the margin that is left after the antennas and cable losses are accounted for.

Where the antenna choice changes the answer

Fresnel clearance sets how high the antennas go. The antenna itself decides how much of the surviving signal you can use. A narrow-beam panel or dish concentrates energy along the path and rejects off-axis reflections that cause multipath; a wide-beam omni radiates into the terrain you just spent money clearing. On longer links, beamwidth and front-to-back ratio matter as much as gain.

If you are still choosing between panel, sector, omni and dish formats for a given band, the antenna selection tool narrows 86 sub-6 GHz models by band, mounting and enclosure size.

Frequently asked questions

What is the first Fresnel zone in one sentence?
It is the ellipsoid-shaped volume around the direct line between two antennas; energy travelling slightly off-axis arrives in phase and adds to the main signal, so obstructions inside that volume reduce the received level and make the link fade more easily.
Why is 60% clearance used instead of 100%?
Because obstruction loss stays very low until roughly 40 to 50 percent of the radius is blocked, then rises sharply. Clearing 60% of the radius keeps the additional loss to well under 1 dB on most paths, while full clearance is rarely achievable on real terrain.
How does the k-factor change the result?
The k-factor scales the effective earth radius. k = 4/3 is the standard temperate-land value; over water, coastal areas and hot humid ground it can fall toward 2/3, which increases the earth bulge and reduces clearance. Run both values when a path grazes terrain or water.
Do I need a Fresnel check on links shorter than 1 km?
Usually the mounting height decides the outcome, not diffraction. At 1 km and 5.8 GHz the mid-path radius is about 3.6 m, so the practical question is whether the antennas clear roofs and parapets. Fresnel calculations matter most on paths longer than one to two kilometres, or where both ends sit low.
Do rain and foliage change the size of the zone?
No. The zone size depends only on frequency and path geometry. Rain and foliage change how much signal survives the path, not how much space the zone occupies, so they belong in the link budget as additional loss rather than in the clearance calculation.

Related tools and pages

Link Budget CalculatorFree-space loss, received power, fade margin and maximum range. EIRP and Power ConverterdBm, watt, dBi and dBd conversions with power density. Antenna SelectorFour inputs, one answer: 86 sub-6 GHz models narrowed to a shortlist. 5G Antennasn78 panel, feedhorn, ceiling and outdoor formats. 4G LTE AntennasWideband 698–2700 MHz panel, omni and sector antennas. Ask an engineerSend the path profile and we will check the clearance for you.

Building a point-to-point link?

Tell us the band, the path length and the mounting arrangement. We will come back with the antenna format, gain and beamwidth that fit the clearance you actually have — not the one the datasheet assumes.

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