Hong Life CalculatorsUnderstanding the Fresnel zone and line-of-sight calculator — concept and principle
A point-to-point radio link (Wi-Fi bridge, microwave backhaul) needs more than a visual line between the antennas. Radio energy travels in an ellipsoid around that line, the first Fresnel zone, and obstacles inside it cause extra loss. The calculator gives the zone radius at an obstacle, the 60% clearance planners keep free, and the Earth's bulge at mid-path.
How it is calculated
- First Fresnel radius: r = 17.32 × √(d₁ × d₂ ÷ (f × D)) in metres, where D is the link length in km, d₁ is the obstacle's distance from one end (km), d₂ = D − d₁, and f is the frequency in GHz.
- 60% clearance: 0.6 × r, the minimum distance the obstacle should stay below the straight line between the antennas.
- Earth bulge at midpoint: h = D² ÷ (8 × 8.5) in metres, which is D² ÷ (8 × k × R) with k = 4/3 and R ≈ 6,370 km, so k × R ≈ 8,500 km.
The principle
The general formula is r = √(λ × d₁ × d₂ ÷ D). Points on the edge of the first zone are those where the path via that point is exactly half a wavelength longer than the direct path. Energy inside that boundary arrives roughly in phase and carries most of the signal, so blocking it weakens the link. Writing λ = 0.3 ÷ f (metres, f in GHz) and using km for the distances gives √300 ≈ 17.32 as the constant. The bulge term accounts for Earth's curvature; refraction bends radio waves slightly downward, modelled with an effective Earth radius 4/3 times the real one.
Worked example
- Inputs: D = 5 km, f = 5.8 GHz, obstacle at d₁ = 2.5 km, so d₂ = 2.5 km.
- d₁ × d₂ ÷ (f × D) = 6.25 ÷ 29 = 0.21552.
- √0.21552 = 0.46424, and 17.32 × 0.46424 = 8.04 m (first Fresnel radius).
- 60% clearance: 0.6 × 8.0406 = 4.82 m.
- Earth bulge: 5² ÷ 68 = 25 ÷ 68 = 0.37 m.
| Frequency (GHz) | 1st Fresnel radius at obstacle (m) |
|---|---|
| 1.45 | 16.08121629 |
| 2.9 | 11.37113709 |
| 4.35 | 9.284494552 |
| 5.8 | 8.040608143 |
| 7.25 | 7.191738555 |
| 8.7 | 6.565129057 |
| 11.6 | 5.685568543 |
How to read the result
Add the clearance and the bulge to the obstacle height (trees, roofs, terrain) and compare the total with the height of the line of sight at that point. If at least 60% of the first zone is clear, extra diffraction loss is usually small. At 0% clearance (the obstacle just touches the line) the loss is typically around 6 dB. Doubling the distance raises the mid-path radius by √2 and the bulge four times.
Common mistakes
- Checking only visual line of sight and ignoring the zone around it.
- Entering the distance in metres or the frequency in MHz; the constant 17.32 assumes km and GHz.
Frequently asked questions
Why 60% and not 100% clearance?
Beyond about 60% of the first zone, extra clearance adds little gain, while full clearance often requires much taller and costlier masts.
Does a higher frequency need less clearance?
Yes. The radius scales with 1 ÷ √f, though rain and foliage hurt higher frequencies more.
Sources: ITU-R Recommendation P.530, Propagation data and prediction methods for the design of terrestrial line-of-sight systems · ITU-R Recommendation P.526, Propagation by diffraction