Fresnel Zone Calculator
Enter the link frequency and distance to calculate the first Fresnel zone radius at its widest midpoint. Switch to the point mode to find the zone radius at any position along the path, check whether an obstruction clears the recommended 60% threshold, or add an earth-curvature correction for long links. All results update instantly in your chosen units.
Formula
Worked example
A 5 GHz link spanning 5 km: wavelength = 0.0600 m. At midpoint, d1 = d2 = 2500 m, so r1 = sqrt(0.0600 x 2500 x 2500 / 5000) = sqrt(75) = 8.66 m. The 60% clearance threshold requires 5.20 m of physical gap. Earth bulge at midpoint with k = 1.33 = (2.5 x 2.5) / (12.74 x 1.33) = 0.37 m.
What is a Fresnel zone?
A Fresnel zone is one of a family of concentric ellipsoids that surround the straight line-of-sight path between two antennas. Radio waves travel not just along the direct path but also in a spread around it, and any obstacle that falls within these ellipsoidal regions can reflect, diffract or absorb energy. The first Fresnel zone, n = 1, is the most important: it contains the bulk of the transmitted energy, and obstructions inside it cause the most signal loss. Higher zone numbers (n = 2, 3 ...) have alternating constructive and destructive effects; clearing the first zone is the primary engineering goal. The zone radius is largest at the midpoint of the link and tapers to zero at each antenna.
The Fresnel zone radius formula
The radius of the nth Fresnel zone at a point that is a distance d1 from antenna A and d2 from antenna B is: rn = sqrt(n x lambda x d1 x d2 / (d1 + d2)), where lambda is the signal wavelength. At the midpoint where d1 = d2 = D/2, this simplifies to r1max = sqrt(lambda x D / 4). In practical RF engineering units, r1max (metres) is approximately 8.66 x sqrt(D (km) / f (GHz)), a convenient approximation for quick field estimates. The calculator uses the exact formula internally for all modes.
How much clearance is needed?
Clearing 60% of the first Fresnel zone radius at every point along the path is the widely cited practical minimum, corresponding to a diffraction loss of roughly 0 dB at that threshold (losses begin to appear only below this value). The ITU-R P.530 recommendation confirms 60% as the minimum for short links; 80-100% clearance is preferred for high-availability backbone links. In point mode this calculator computes the earth-bulge correction using the standard k = 4/3 atmosphere, which bends the effective path and makes the earth appear flatter. Add the bulge figure to any obstacle height when assessing whether a ground-level feature clears the zone.
Obstruction clearance and earth curvature
For links longer than about 5 km, the curvature of the earth causes the mid-path ground level to bulge upward relative to a straight geometric line. The earth-bulge formula in metres is: bulge = (d1 x d2) / (12.74 x k), where d1 and d2 are distances from the two ends in km and k is the atmospheric refractivity ratio (1.33 for a standard atmosphere, 1.0 for geometric flat-earth, smaller in extreme dry conditions). In obstruction mode this calculator subtracts the bulge from the effective line-of-sight height before comparing it to the obstacle, giving a physically correct clearance assessment. A negative clearance margin means the obstruction falls inside the zone.
Fresnel zone clearance guidelines
| Clearance (% of r1) | Link quality | Typical use case |
|---|---|---|
| < 40% | Poor - significant diffraction loss | Avoid |
| 40-59% | Marginal - noticeable degradation | Temporary or low-priority |
| 60% | Acceptable minimum (ITU-R standard) | Most enterprise links |
| 80% | Good - diffraction loss < 1 dB | Preferred for critical links |
| 100% | Excellent - full free-space path loss | Mission-critical backhaul |
Industry-accepted clearance thresholds for point-to-point wireless links. The 60% threshold is the practical minimum; higher values are preferred for mission-critical links.
Frequently asked questions
What is the first Fresnel zone and why does it matter?
The first Fresnel zone is an ellipsoid of revolution around the direct path between two antennas. Energy that travels paths longer than the direct path by up to half a wavelength (n = 1) arrives constructively; energy reflected or diffracted from objects inside this zone can add or subtract, but obstructions inside it cause the most loss. Clearing the first zone is the primary goal of wireless link design.
How much Fresnel zone clearance do I need?
A minimum of 60% of the first Fresnel zone radius is the widely accepted practical standard for enterprise wireless links. This corresponds to roughly 0 dB of additional diffraction loss at that margin. For high-availability point-to-point backhaul, 80-100% is recommended. Below 40% clearance, links experience measurable degradation.
Does higher frequency give a smaller Fresnel zone?
Yes. Because wavelength decreases as frequency increases, the Fresnel zone radius is proportional to the square root of wavelength, so higher frequencies produce narrower ellipsoids. A 5 GHz link has a midpoint radius that is about 40% narrower than a 2.4 GHz link over the same distance, making it somewhat easier to clear in urban environments with nearby buildings.
How do I account for earth curvature in my link calculation?
Use the earth-bulge formula: bulge (metres) = (d1 x d2) / (12.74 x k), where d1 and d2 are km distances from each end to the point and k = 1.33 for a standard atmosphere. This calculator applies the correction automatically in Point and Obstruction modes. For links under about 5 km the bulge is typically under 0.5 m and may be ignored; for long rural links of 20 km or more it can exceed 5 m and must be included.
What does the nth Fresnel zone tell me?
Higher zones (n = 2, 3, 4 ...) have alternating effects: objects in even zones (n = 2, 4 ...) can actually add a small amount of signal through constructive interference, while odd zones (n = 1, 3 ...) are destructive when partially obstructed. In practice, only the first zone matters for link budgets because the energy contribution of higher zones drops off rapidly. The nth zone radius is sqrt(n) times the first zone radius at the same point.
What happens when an obstruction falls inside the Fresnel zone?
Any object inside the first Fresnel zone diffracts and scatters some of the signal energy, reducing the signal level at the receiver. The amount of loss depends on how deeply the obstacle penetrates the zone: an object at the zone boundary (100% clearance) causes negligible loss, one at 60% clearance causes roughly 0 dB of extra loss (the breakeven point), and an object at 0% (grazing the line of sight) causes about 6 dB of diffraction loss on top of free-space path loss.