The Fresnel zone calculator above answers the question that decides whether a point-to-point radio link works: how much space around the straight line between two antennas has to be kept clear? The answer is never zero, and on a long path at a low frequency it can be tens of metres.
Arb Digital builds free physics calculators that each own one job. The free space path loss calculator tells you how much signal a path costs when nothing is in the way; this page tells you what "nothing in the way" actually requires. The two are used together, because a link budget that assumes free-space loss is only valid if the Fresnel clearance is there to support it.
What This Fresnel Zone Calculator Does
A Fresnel zone is a three-dimensional ellipsoid with the two antennas at its foci. The first zone contains every path whose length exceeds the direct line by less than half a wavelength; the second contains those between half a wavelength and a full one, and so on outward. Energy arriving by a route in the first zone is broadly in phase with the direct ray and reinforces it. Energy from the second zone arrives out of phase and cancels it.
The tool computes the radius of any zone at any point along the path, the widest point of the first zone, and the clearance figure a link is normally planned against. It also computes the earth bulge at the same point, because on paths beyond a few kilometres the curvature of the ground eats into the clearance before any tree or building does.
The zone is fattest at the middle of the path and tapers to nothing at each antenna. That shape matters for practical planning: an obstacle near one end has to be very close to the sight line to cause trouble, while the same obstacle halfway along may need to be many metres below it.
How to Use It
- Enter the operating frequency. Wavelength is what sets the zone size, and the tool reports it so you can sanity-check the scale.
- Enter the total path length between the two antennas. Kilometres, metres or miles — the distance to the point of interest uses the same unit.
- Set the distance to the point you care about. Half the path length gives the widest part of the zone; a specific obstacle's distance gives the clearance needed there.
- Leave the zone number at one unless you are studying interference. Zone one is what link planning uses; higher zones matter when you are analysing reflections and multipath.
- Add the earth bulge to the clearance figure. The note under the grid does this for you and reports the total height the sight line must sit above the terrain at that point.
The Formula: How Fresnel Zone Radius Is Calculated
The radius of the nth Fresnel zone at a point that is d1 from one antenna and d2 from the other is rn = √(nλd1d2 ÷ (d1 + d2)), with everything in metres. This is the standard result of Fresnel–Kirchhoff diffraction theory applied to a path with a single obstruction, and it is the basis of the obstacle-loss method in ITU-R Recommendation P.526, "Propagation by diffraction", which sets out how diffraction loss is computed from the ratio of obstacle height to zone radius.
Two useful special cases follow. At the midpoint, d1 = d2 = D/2, and the expression collapses to r = ½√(nλD), the widest the zone ever gets. And because wavelength is c divided by frequency, the whole thing can be written for the first zone as r = 8.657√(D/f) with D in kilometres, f in gigahertz and r in metres — the shortcut most link planners carry in their heads.
The earth bulge at the same point is h = d1d2 ÷ (2kR), where R is the earth's radius and k is the effective-earth factor that accounts for atmospheric refraction bending the beam slightly downward. The customary value of four thirds and the clearance criteria built on it are described in ITU-R Recommendation P.530 on terrestrial line-of-sight systems, which also covers how that factor varies with climate and how sub-refractive conditions erode a clearance that looked adequate on paper.
Work the defaults by hand. At 2.4 GHz the wavelength is 299,792,458 ÷ 2.4 × 109 = 0.12491 m. On a 10 km path, at the 5 km midpoint, r1 = √(0.12491 × 5000 × 5000 ÷ 10,000) = √312.3 = 17.67 m. The shortcut agrees: 8.657 × √(10 ÷ 2.4) = 17.67 m. Sixty per cent of that is 10.60 m. The earth bulge with k = 4/3 is 5000 × 5000 ÷ (2 × 1.333 × 6,371,000) = 1.47 m, so the sight line needs to clear the ground at the midpoint by about 12.07 m in total.
Why Sixty Per Cent and Not One Hundred
The figure everyone quotes is that 60 per cent of the first Fresnel zone must be clear. It is not arbitrary, and it is not a safety margin in the ordinary sense. Diffraction loss over a knife-edge obstacle is essentially zero once the obstacle sits below about 0.6 of the first zone radius; blocking the outer 40 per cent costs almost nothing.
Push further and the loss climbs quickly. An obstacle exactly on the sight line — a grazing path, zero clearance — costs about 6 dB, which is a factor of four in power lost to something that has not physically blocked anything. Beyond that, into genuine shadow, the loss grows steeply and unpredictably.
There is a subtlety worth knowing. Clearance above 0.6 does not give a smooth improvement toward zero loss. Because the zone boundaries alternate in phase, the received signal oscillates slightly above and below the free-space value as clearance increases, peaking a little above it near the edge of the first zone. Planning to 60 per cent puts you safely past the region where diffraction bites without chasing a marginal ripple.
Frequency, Path Length and Where the Trouble Is
Zone radius grows as the square root of wavelength and as the square root of path length. Both dependencies are gentler than people expect, and both point the same way: long, low-frequency links need enormous clearance.
Compare two links. A 5 GHz path of 3 km has a first zone radius of 6.7 m at the midpoint — clearing a hedge is usually enough. A 150 MHz path of 40 km has a radius of 141 m, which is taller than almost anything on the route and generally impossible to achieve on flat terrain. This is exactly why long low-band links are planned as diffraction paths from the start rather than as clear ones, and why microwave backhaul lives on hilltops.
Doubling the frequency shrinks the radius by only 30 per cent, so moving band is a weak lever. Halving the path length by inserting a relay is far more effective, because it cuts both the zone radius and the earth bulge, and the bulge falls with the square of the hop length rather than its square root. Our wavelength calculator and frequency converter handle the band arithmetic behind these comparisons.
What the Calculation Does Not Cover
The zone geometry is exact, but the clearance it implies is only one of several things that decide whether a link stays up. Refraction is variable: the four-thirds earth is an average, and under sub-refractive conditions the effective bulge grows and a path planned to the minimum can fail for hours at a time.
Reflections are the other omission. A path over water or flat ground produces a strong reflected ray, and whether it reinforces or cancels the direct one depends on the path-length difference — which is precisely what the zone structure describes. A link with perfect first-zone clearance can still fade deeply if the ground reflection arrives out of phase, which is why over-water paths are treated as a special case.
Finally, vegetation is not a knife edge. A tree line attenuates by absorption and scattering through its depth rather than diffracting cleanly over an edge, and it changes with season and moisture. Treat a wooded obstruction as a loss to be measured rather than a height to be cleared. For the rest of the link budget, use the free space path loss calculator and the EIRP calculator; for the horizon geometry on longer paths, the radar horizon calculator covers the same refraction assumption applied to visibility rather than clearance.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating line of sight as sufficient — you can see the far antenna clearly and still lose most of the signal to an obstacle sitting inside the first zone.
- Using the midpoint radius everywhere — the zone tapers to nothing at each antenna, so an obstacle near one end needs far less clearance than the same obstacle halfway along.
- Forgetting the earth bulge — on paths beyond about ten kilometres the curvature of the ground can demand more clearance than the Fresnel zone itself.
- Mixing units in the radius formula — the square-root expression needs all distances in metres. The 8.657 shortcut is the one that takes kilometres and gigahertz, and the two are not interchangeable.
- Assuming refraction is constant — the four-thirds earth factor is a long-term average, and sub-refractive weather can push a marginally planned path into failure.
Related Free Tools From Arb Digital
Pair this with the free space path loss calculator for the loss side of the link budget and the EIRP calculator for transmitted power. Band arithmetic is handled by the wavelength calculator and the frequency converter, antenna sizing by the dipole antenna calculator, and horizon geometry on long paths by the radar horizon calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It is an ellipsoid of space around the straight line between two antennas, with the antennas at its foci. The first zone holds every indirect path that is less than half a wavelength longer than the direct one, and energy arriving through it reinforces the signal.
Sixty per cent of the first zone radius is the usual planning figure. Below that, diffraction loss over an obstacle starts to become significant; above it, the loss is essentially zero.
At the midpoint of the path. The radius there is half the square root of the wavelength times the path length, and it tapers to zero at each antenna.
Yes, but only weakly. Radius falls with the square root of wavelength, so doubling the frequency shrinks the zone by about 30 per cent. Shortening the path is a far more effective lever.
It is the height by which the curved earth rises above the straight chord between two points. On paths longer than about ten kilometres it can consume more of the clearance budget than the Fresnel zone does.
Because the atmosphere refracts radio waves slightly downward under normal conditions, so they follow the terrain further than straight lines would. Scaling the earth radius by four thirds lets the paths be drawn straight while keeping the geometry correct.
You lose about six decibels, a factor of four in power, even though nothing is physically blocking the view. Diffraction loss rises steeply once the obstacle goes above the line into genuine shadow.
Not for basic clearance planning, which only concerns zone one. They matter when analysing reflections, because energy from even-numbered zones arrives out of phase with the direct ray and can cancel it.
This tool is provided for educational and study use. It gives ideal Fresnel geometry and a standard-refraction earth bulge, and does not model terrain profiles, vegetation loss, ground reflections, rain fade or variable refraction, so treat its output as a planning aid rather than a link design or licensing calculation.
