Fresnel zone calculator
The Fresnel zone is the rugby-ball-shaped volume around the direct line between two antennas that carries most of the radio energy. A link needs at least 60% of the first zone clear of obstacles, or it loses signal even when the antennas can “see” each other. This calculator gives the radius at any point of the path.
Where the obstacle sits: 50% = mid-path, where the zone is widest.
The green ellipse is the first Fresnel zone stretched between masts A and B. The dashed amber ellipse marks 60% of it, the minimum that must stay clear. The vertical marker reads off the radius at the chosen position along the path.
Assumes a straight path in free space. Real clearance is measured against terrain, buildings and vegetation along the path, minus the Earth bulge on long links.
How it works
- 01
Find the wavelength
λ = c / f. At 5.8 GHz the wavelength is about 5.2 cm; at 900 MHz it is 33 cm. Lower frequencies need more clearance, because the zone radius grows with the square root of the wavelength.
- 02
Apply the Fresnel radius formula
The first-zone radius at a point d₁ from one antenna and d₂ from the other is r1 = λ·d1·d2 / (d1 + d2) . The zone is an ellipse: widest at mid-path, shrinking to zero at each antenna.
- 03
Apply the 60% rule
Engineering practice keeps at least 0.6 × r₁ free of obstructions — trees, roofs, terrain. With less clearance, diffraction loss rises long before the direct line is actually blocked; a fully clear first zone behaves essentially like free space.
- 04
Account for earth curvature and terrain
Beyond roughly 10 km the Earth bulge rises into the zone and adds to every obstacle height. The terrain along the real path decides the rest — check an elevation profile instead of assuming flat ground.
Formulas
- rn — zone radius, m
- λ — wavelength, m (λ = c / f)
- d1, d2 — distances to the two antennas, m
- d1, d2, d — km, with d = d1 + d2
- f — frequency, GHz
Worked example
- λ = 299 792 458 / 5.8×109 = 0.0517 m
- d1 = d2 = 5 000 m
- r1 = 0.0517 · 5 000 · 5 000 / 10 000 = 11.4 m
- 60% clearance: 0.6 · 11.4 = 6.8 m
- → keep a roughly 7 m radius around the sight line free at mid-path
FAQ
- How much Fresnel zone clearance does a link need?
- At least 60% of the first Fresnel zone radius, measured from the straight line between the antennas. A fully clear first zone is ideal; below 60% clearance, diffraction loss rises steeply even though the path is optically clear.
- Why does a link fail even with clear line of sight?
- Radio energy travels through a volume, not a line. An obstacle inside the first Fresnel zone — a tree line, a rooftop, the ground itself — absorbs and diffracts part of the wave, and reflected components can arrive out of phase and cancel the direct signal.
- Does the Fresnel zone get bigger or smaller with frequency?
- Smaller. The radius scales with the square root of the wavelength: a 900 MHz link over 10 km needs about 29 m of mid-path clearance for the full first zone, while a 5.8 GHz link needs about 11 m. That is one reason microwave links tolerate tighter corridors.
- Where along the path is the Fresnel zone widest?
- At the midpoint, where r1 = ½·λ·d. It tapers to zero at each antenna — the same obstacle matters far more in the middle of the path than near either end.
The formula tells you how much clearance the link needs. Whether the terrain actually provides it is a map question — Waveshed draws line-of-sight over real elevation data, free in your browser.
Check your path on the map →Related guides
- Elevation profile & measuring tools — the simulator’s side view draws LOS and the 0.6·F₁ Fresnel band over real terrain
- LOS vs RF — which analysis do you need? — when clearance is enough and when full RF modeling is
Sources & further reading
- ITU-R Recommendation P.526 — Propagation by diffraction ↗ — defines Fresnel ellipsoids and diffraction over obstacles
- ITU-R Recommendation P.530 — Propagation data for terrestrial line-of-sight systems ↗ — clearance design criteria used in microwave link planning
- Fresnel zone — Wikipedia ↗ — derivation, geometry and illustrations
Related tools
Free-space path loss calculator
Signal loss over distance for any frequency, from the FSPL formula.
Earth bulge calculator
Height the Earth’s curvature adds mid-path, with k-factor refraction.
Radio horizon calculator
How far a signal reaches over smooth earth, from antenna height.
Knife-edge diffraction calculator
Extra loss when a ridge or roof cuts into the path, from the ITU-R P.526 single-edge model.