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Fresnel Zone Calculator

Calculate Fresnel zone radius and required clearance for RF line-of-sight links. Determine obstruction margins for microwave and WiFi paths. Free, instant results.

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Formula

rn=nλd1d2d1+d2r_n = \sqrt{\frac{n \lambda d_1 d_2}{d_1 + d_2}}
r_n— nth Fresnel zone radius (m)
n— Zone number
λ— Wavelength (m)
d1, d2— Distances from endpoints to midpoint (m)

How It Works

Fresnel zone calculator determines the clearance radius required around the direct line-of-sight path to avoid diffraction loss from obstructions — wireless network planners, microwave link engineers, and point-to-point system designers use this to ensure reliable propagation. The first Fresnel zone radius r1 = sqrt(n lambda d1 * d2 / d) determines the critical clearance volume per ITU-R P.530-17.

Obstructing more than 40% of the first Fresnel zone (0.6 * r1 clearance) introduces diffraction loss of 0 dB; obstructing 60% adds approximately 6 dB loss per knife-edge diffraction theory. A 10 km link at 5.8 GHz has first Fresnel zone radius of 14.3 m at mid-path — a 9 m tall obstacle at the halfway point obstructs 63% of the zone, causing approximately 6 dB additional path loss beyond free-space prediction.

According to Skolnik's 'Radar Handbook' and ITU-R P.526, Fresnel zone clearance requirements scale with sqrt(wavelength * distance). Lower frequencies require larger clearance: at 900 MHz the first Fresnel zone radius is 2.5x larger than at 5.8 GHz for the same path length. This explains why sub-GHz IoT networks tolerate more foliage and terrain obstruction than microwave links.

Worked Example

Problem: Determine antenna heights for a 15 km microwave backhaul link at 18 GHz crossing a 30 m hill located 6 km from the near end.

Solution per ITU-R P.530-17 methodology:

  1. Calculate wavelength: lambda = 3e8 / 18e9 = 0.0167 m (16.7 mm)
  2. Distance from near antenna to obstacle: d1 = 6 km = 6000 m
  3. Distance from obstacle to far antenna: d2 = 15 - 6 = 9 km = 9000 m
  4. First Fresnel zone radius at obstacle: r1 = sqrt(1 0.0167 6000 * 9000 / 15000) = 7.75 m
  5. Required clearance (60% of r1): 0.6 * 7.75 = 4.65 m above obstacle
  6. Line-of-sight height at obstacle: h_los = 30 + 4.65 = 34.65 m above ground
  7. Antenna height calculation (assuming flat terrain endpoints):
- Near antenna height: h1 = 34.65 * (15000/6000) = 86.6 m - Far antenna height: h2 = 34.65 * (15000/9000) = 57.8 m
  1. Practical adjustment: Use 90 m and 60 m towers with 3 m clearance margin for Earth curvature (K=4/3) and vegetation growth.
At 6 GHz (lower frequency), r1 = 13.4 m, requiring h_los = 38 m — demonstrating frequency-clearance tradeoff.

Practical Tips

  • ✓Ensure 60% first Fresnel zone clearance (0.6 * r1) for near-lossless propagation; 80% clearance provides 3 dB margin for vegetation growth and atmospheric variations
  • ✓Use terrain profile tools (Google Earth Pro elevation profile, RF planning software) to identify all obstacles along the path, not just the obvious ones
  • ✓Account for seasonal vegetation changes — deciduous trees in leaf add 0.4-0.8 dB/m penetration loss at UHF per ITU-R P.833; a 20 m canopy in the Fresnel zone can add 10+ dB seasonal loss

Common Mistakes

  • ✗Assuming optical line-of-sight is sufficient — visual clearance ignores the Fresnel volume; a link may have clear LOS but lose 6+ dB to Fresnel obstruction from ground reflection or nearby structures
  • ✗Using incorrect distance values — d1 and d2 are distances from obstacle to each antenna, not total path length; maximum r1 occurs at mid-path where d1 = d2
  • ✗Ignoring Earth curvature on long paths — Earth bulge at mid-path of 20 km link is 7.8 m (K=4/3 atmosphere); combined with Fresnel clearance, this significantly impacts antenna height requirements
  • ✗Calculating for single worst-case obstacle only — profile the entire path; multiple partial obstructions have cumulative effect per ITU-R P.526 diffraction model

Frequently Asked Questions

Wave propagation is not confined to a geometric ray — energy spreads across the Fresnel volume. Obstruction causes diffraction loss following Huygens-Fresnel principle: 0 dB loss at 60% clearance, 6 dB at knife-edge (50% obstruction), 15-20 dB for complete blockage. A link designed to free-space path loss but lacking Fresnel clearance will underperform by 6-20 dB, potentially causing intermittent failures. ITU-R P.530 requires Fresnel analysis for all microwave link designs.
Diffraction loss increases approximately linearly with obstruction depth per ITU-R P.526: 0 dB at 0.6*r1 clearance, 6 dB at grazing (0% clearance), 16 dB at -0.5*r1 (obstacle 0.5*r1 into zone), 22 dB at -1.0*r1. Complete blockage causes 20+ dB loss. Multiple obstacles along path have cumulative effect calculated by cascaded knife-edge or cylinder diffraction models. In practice, obstructed links experience intermittent fading as refractivity changes the effective ray path.
First Fresnel zone radius scales as sqrt(lambda): r1 proportional to sqrt(c/f). At mid-path of 10 km link: 900 MHz: r1 = 28.9 m; 2.4 GHz: r1 = 17.7 m; 5.8 GHz: r1 = 11.4 m; 18 GHz: r1 = 6.5 m. Lower frequencies require larger clearance but penetrate foliage better — the net effect often favors sub-GHz for obstructed environments despite larger theoretical Fresnel zone.
Yes, but urban propagation involves multiple diffraction edges and reflections. ITU-R P.1411 provides urban models where Fresnel-based diffraction loss is one component alongside building penetration, street canyon waveguiding, and multipath. For rooftop-to-rooftop links, standard Fresnel analysis applies. For street-level, empirical models (Okumura-Hata, COST-231) incorporate aggregate effects without explicit Fresnel calculation.
Required antenna height = obstacle height + Fresnel clearance + Earth curvature (for long paths). For a 50 m obstacle at mid-path of 20 km, 5.8 GHz link: r1 = 16.1 m, 60% clearance = 9.7 m, Earth bulge = 7.8 m (K=4/3). Required LOS height = 50 + 9.7 + 7.8 = 67.5 m. Antenna heights depend on obstacle position — obstacles near endpoints require lower clearance because d1*d2 product is smaller. Path profiling identifies the controlling obstacle determining minimum heights.

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