Fresnel Zone Calculator

Introduction to Fresnel-zone clearance for terrestrial radio links

Fresnel-zone clearance describes the space a radio wave needs around the direct line between two antennas. A visible line of sight is useful, but it is not the whole propagation path: energy also travels through an ellipsoidal volume around that line. When a ridge, roof, tree, crane, or other object enters the first Fresnel zone, part of the wavefront is blocked and the received signal can suffer diffraction loss and deeper fading.

This Fresnel zone calculator checks one chosen point on a terrestrial link. It finds the radius of the selected Fresnel zone, the usual 60% first-zone clearance target, and the effective-earth bulge at that point. If you also enter the vertical gap from an obstacle to the direct ray, it estimates ideal knife-edge diffraction loss. The calculation is therefore useful for comparing mast heights, testing a rooftop obstruction, or checking a station from a terrain profile before a full design study.

Position matters. The zone is narrow close to either antenna and widest near the midpoint, where the distances to both sites are similar. Earth curvature follows the same general pattern but becomes much more important on long hops. A flat-earth Fresnel result can look acceptable while curvature raises the terrain into the required clearance corridor, particularly on microwave links several tens of kilometres long.

How to use the Fresnel-zone and earth-bulge calculator

Enter d₁ as the distance from the checkpoint to site A and d₂ as the distance from that checkpoint to site B. Select one distance unit for both values. The calculator adds them to obtain the total path length, so do not put the full hop length into either box. For example, a ridge 4 km from site A on a 12 km path uses d₁ = 4 km and d₂ = 8 km.

Next, enter the radio frequency and select MHz or GHz. The calculation converts all measurements internally to metres and hertz, which avoids the common thousand-fold unit error. Use zone order n = 1 for clearance planning. Higher zones can be useful when discussing reflected paths, but the first zone is the practical obstruction screen. The effective earth-radius factor k defaults to 1.333, approximately 4/3, the standard-atmosphere median commonly used by ITU-R guidance.

Ray clearance is optional. It is the vertical distance from the obstacle top up to the direct ray: use a positive value when the ray passes above the obstacle and a negative value when the obstacle projects above it. The clearance field uses the selected result unit. After computing, compare the real surveyed clearance with the reported earth bulge plus 60% of the first-zone radius. The full 1.0 F₁ figure is also shown as a more conservative median-k screening target.

Fresnel radius, wavelength, and clearance formulas

The calculator uses the full Fresnel-radius equation rather than a midpoint shortcut. In the formula, λ is wavelength, d₁ and d₂ are distances from the checkpoint to the endpoints, and n is the zone order. All terms must use self-consistent units. Because the product d₁d₂ is largest relative to d₁ + d₂ at the centre of a fixed path, the radius peaks near the midpoint.

The speed of light c is 299 792 458 m/s, and frequency f is in hertz. A lower frequency has a longer wavelength and therefore a wider Fresnel corridor. At the midpoint, the engineering form for the first zone is commonly written as follows, with distances in kilometres, frequency in GHz, and the result in metres.

The familiar midpoint-only shortcut follows from that same relationship. It is a useful cross-check when d₁ and d₂ are equal, but it should not be used at an off-centre obstacle.

Effective-earth bulge for the selected k-factor

A straight ray between two antenna heights is a chord, while terrain follows the curved effective earth. The k-factor scales the earth radius to model normal atmospheric refraction. With distances in kilometres and the bulge in metres, the practical approximation used here is:

Smaller k values produce a larger apparent bulge and can represent more demanding sub-refractive conditions. The formula is a terrestrial small-angle approximation, not a satellite-path model. It also does not supply terrain elevation; it tells you how much the earth rises relative to the chord, which must be added to a surveyed obstacle profile.

Knife-edge diffraction loss from the entered obstacle clearance

For the optional obstruction check, the calculator converts the positive ray clearance into the ITU-R P.526 knife-edge sign convention: an obstacle below the ray has negative h. The dimensionless parameter ν is then:

For ν greater than −0.78, the ideal single-knife-edge loss approximation is:

A 60% first-zone clearance corresponds to approximately zero knife-edge loss in this ideal model, which is why it is a common planning threshold. The page also reports the simple P.530 average-terrain estimate below. Broad hills, multiple obstacles, and vegetation are not ideal knife edges, so treat this as a screening result rather than a promised fade margin.

Worked example: a 12 km, 6 GHz ridge crossing

Consider a 12 km, 6 GHz path with a ridge 4 km from site A. Enter d₁ = 4 km, d₂ = 8 km, n = 1, k = 1.333, and metres as the result unit. The wavelength is about 0.04997 m. The first Fresnel radius at the ridge is about 11.54 m, so the 60% clearance target is 6.92 m.

The effective-earth bulge at the same point is about 1.88 m. A terrain-profile designer therefore needs roughly 8.80 m between the chord and the surveyed ridge top to satisfy the 60% geometry target under the selected k-factor. If the direct ray clears the ridge by only 5 m, the path has 43% of F₁ clearance. It is visible but inside the diffraction zone, and the calculator will show a modest loss estimate rather than calling it a free-space path.

The lever arm also helps with mast decisions. Raising site A moves the ray at the ridge by d₂/(d₁+d₂), or two-thirds of the mast increase. Raising the farther site B moves it by only one-third. This does not replace a profile calculation, but it quickly identifies which end has the more efficient height adjustment.

Reading Fresnel-zone results during mast siting

Use the result as a geometric requirement, not as the final statement that a link will work. The reported bulge plus clearance target must be compared with an actual profile that includes terrain, buildings, tree height, and survey uncertainty. Check several stations, especially the midpoint and every significant obstruction, because a single checkpoint cannot discover another ridge farther along the path.

For early screening, 60% of F₁ is a practical threshold. For a more conservative median-atmosphere check, use the displayed 1.0 F₁ requirement. For an operational design, apply the relevant ITU-R procedure and local refractivity data, then include link budget, fade margin, antenna pattern, rain, atmospheric absorption, interference, and maintenance growth allowances. A tree line that is clear today may not remain clear after seasonal growth or wind movement.

Limitations of this Fresnel clearance estimate

This Fresnel-zone calculator intentionally evaluates one point and one effective k-factor. It does not model a full terrain profile, multiple diffraction edges, rounded obstacles, reflections, clutter attenuation, or time-varying atmospheric layers. Knife-edge loss is commonly optimistic for a broad ridge, while a fixed k-factor cannot represent ducting or the worst-month refractivity distribution for a particular route.

It also does not perform a radio link budget. Free-space path loss, transmitter power, feeder loss, antenna gain, receiver threshold, rain attenuation, gaseous absorption, multipath, polarization effects, and interference may determine feasibility even where the first zone is clear. Conversely, an obstruction can sometimes be accepted only after its loss has been budgeted with appropriate engineering margin.

Use consistent distances to the same checkpoint, and remember that Fresnel radius is not a tower height. It is the radius around a ray whose elevation comes from the antenna heights and the path profile. Long, expensive, regulated, or service-critical links should be surveyed and reviewed with suitable propagation and reliability tools before steel is ordered.

Frequently asked questions about Fresnel-zone clearance

Sources for the radio-path formulas

The Fresnel-radius, diffraction-zone, diffraction-parameter, and knife-edge relationships are based on ITU-R Recommendation P.526, Propagation by diffraction. The 60% planning criterion, effective-earth discussion, and terrestrial line-of-sight design context are based on ITU-R Recommendation P.530. Refractivity background is available in ITU-R Recommendation P.453.