Fresnel Zone Calculator
Created by: Olivia Harper
Last updated:
Determine how much clearance your VHF, UHF, or microwave link needs above terrain and obstacles. Visualize the full Fresnel zone profile from TX to RX.
Fresnel Zone Calculator
Amateur RadioCalculate the Fresnel zone radius at any point along a radio path to determine required obstacle clearance for reliable VHF/UHF/microwave links.
Note: These results are for guidance only and shouldn't be taken as professional advice. Always double-check with a qualified expert before making decisions.
What is a Fresnel Zone Calculator?
A Fresnel zone is one of a family of concentric ellipsoids that surround the direct line-of-sight path between a transmitting and receiving antenna. Any obstacle that penetrates the innermost ellipsoid — the 1st Fresnel zone — diffracts some of the radio energy away from the receiver, adding signal loss that is not predicted by free-space path loss alone. For licensed amateurs operating VHF, UHF, or microwave links, understanding Fresnel zone geometry is essential to building reliable point-to-point paths rather than relying on guesswork about antenna height.
The 1st Fresnel zone is defined as the set of all points in space where the sum of the distances to both antennas exceeds the direct path length by exactly half a wavelength (λ/2). Energy reflected or diffracted from the boundary of this zone arrives at the receiver 180° out of phase with the direct wave and causes cancellation. The 2nd zone boundary represents a full wavelength (λ) path-length excess; energy from this zone arrives in phase and can add constructively. Each successive zone alternates between destructive and constructive interference, but the contribution of each zone diminishes rapidly.
For most practical VHF and UHF links — 2m weak-signal DX, 70cm terrestrial, AREDN mesh nodes, 10 GHz microwave contest paths — the critical design question is whether the 1st Fresnel zone is sufficiently clear of terrain, trees, buildings, and structures. Industry practice and ITU-R guidance both accept that maintaining at least 60% of the 1st Fresnel zone radius free of obstructions keeps the additional diffraction loss below 0.5 dB. Losing that clearance can add 6 dB or more to path loss — the equivalent of cutting transmitter power by 75%.
The Fresnel zone radius is largest at the geometric midpoint of the path and tapers to zero at each antenna. This means mid-path obstacles are the most critical, while obstructions close to either end have minimal effect. For a 50 km path at 146 MHz, the mid-path 1st Fresnel radius reaches approximately 160 m. At 1296 MHz the same path has a mid-path radius of about 54 m, and at 10 GHz it narrows to about 19 m — illustrating why microwave links on longer paths are generally easier to clear than VHF links on similar terrain.
How the Fresnel Zone Calculator Works
The 1st Fresnel zone radius at a point along the path is computed from r₁ = √(λ × d₁ × d₂ / (d₁ + d₂)), where λ is the free-space wavelength (c/f), d₁ is the distance from the transmitter to the obstacle point, d₂ is the distance from that point to the receiver, and d₁ + d₂ equals the total path length. The wavelength is derived automatically from the entered frequency: λ(km) = 299792.458 / (f(MHz) × 10⁶). For the nth Fresnel zone the radius is simply rₙ = √n × r₁, so the 2nd zone has radius √2 × r₁ and the 3rd zone √3 × r₁.
The calculator steps through 60 evenly spaced points along the path and computes r₁ at each point, producing the ellipse profile shown in the chart. The 60% clearance line — plotted separately — is 0.6 × r₁ at each point and represents the minimum height above any obstacle that must be maintained. At the ends of the path (d₁ = 0 or d₂ = 0) the radius collapses to zero, which is why antenna locations are always inside the zone regardless of height. The obstacle position input sets the specific point where the clearance figures displayed in the summary cards are computed.
To translate zone radius into a tower height requirement, you need to know the terrain height at the obstacle location relative to your antennas. If the LOS line between TX and RX antennas passes 30 m above a hilltop at the obstacle position, and the 60% clearance threshold at that point is 45 m, you need the LOS line to rise 15 m — meaning you either raise one antenna, use a path that clears the hill, or accept the additional diffraction loss. This is why terrain profile tools such as SPLAT!, Radio Mobile, or HeyWhatsThat are used alongside this calculator in professional path engineering.
Fresnel zone formulas
r₁(d) = √(λ × d₁ × d₂ / (d₁ + d₂)) [1st Fresnel zone radius at obstacle]
rₙ = √n × r₁ [nth Fresnel zone radius]
λ = c / f = 299792.458 km/s / (f_MHz × 10⁶) [wavelength in km]
d₁ + d₂ = D (total path length)
Maximum r₁ occurs at midpoint: d₁ = d₂ = D/2
r₁_max = √(λ × D / 4) [mid-path maximum radius]
60% clearance required: h_clear ≥ 0.6 × r₁ (<0.5 dB additional loss)
100% clearance: free-space propagation maintained
Example Calculations
146 MHz, 50 km path, mid-path obstacle
λ = 299792.458 / (146 × 10⁶) = 0.002053 km. At the midpoint: d₁ = d₂ = 25 km. r₁ = √(0.002053 × 25 × 25 / 50) = √(0.02566) = 0.1602 km = 160.2 m. 60% clearance required = 96.1 m. Any terrain feature within ~96 m of the LOS line at the midpoint will noticeably degrade link performance.
1296 MHz, 100 km path, obstacle at 30 km from TX
λ = 299792.458 / (1296 × 10⁶) = 0.0002313 km. d₁ = 30 km, d₂ = 70 km. r₁ = √(0.0002313 × 30 × 70 / 100) = √(0.004857) = 0.06969 km = 69.7 m. 60% threshold = 41.8 m. Because the obstacle is off-center the zone is smaller than at mid-path; the worst-case point at 50 km gives r₁ = 76.0 m.
10 GHz (10000 MHz), 20 km path, mid-path obstacle
λ = 299792.458 / (10000 × 10⁶) = 0.00002998 km. At midpoint: d₁ = d₂ = 10 km. r₁ = √(0.00002998 × 10 × 10 / 20) = √(0.001499) = 0.03872 km = 38.7 m. 60% clearance = 23.2 m. At 10 GHz even a modest rooftop or treetop at the path midpoint can block 6+ dB of signal, making careful siting essential for microwave links.
Common Amateur Radio Uses
- VHF/UHF weak-signal DX path engineering — determining minimum tower heights to clear terrain on 2m, 70cm, and 23cm links
- AREDN (Amateur Radio Emergency Data Network) mesh node placement — ensuring each hop has adequate Fresnel clearance for reliable digital throughput
- Microwave contest and EME path analysis — qualifying 3.4 GHz, 5.7 GHz, and 10 GHz paths before investing in dish construction
- SOTA and POTA portable operation — quickly checking whether a planned portable site has line-of-sight with sufficient clearance to the target station
- Repeater link engineering — verifying that a proposed repeater-to-link-site path clears intervening terrain and maintains the 60% Fresnel rule
- Amateur television (ATV) and DATV path planning — ATV is particularly sensitive to path degradation and rewards careful Fresnel analysis before construction
Tips for Better Ham Radio Planning
The 60% clearance rule is a minimum, not a target. Whenever terrain and antenna height allow, aim for full 1st Fresnel zone clearance (100%) — this maximizes received signal and provides margin for seasonal vegetation growth, which can reduce effective clearance by 10–15 m in dense deciduous forest. For critical links carrying digital data, even temporary leaf-on blockage into the 1st Fresnel zone can cause packet loss and link outages that are difficult to diagnose without a path analysis on hand.
Always calculate Fresnel clearance at the worst-case point, which is not necessarily the highest terrain feature. A low ridge at the mid-path will demand more clearance height (because the Fresnel zone is widest there) than a taller ridge close to either antenna. Step through the obstacle position slider to find the point along your path where the ratio of terrain penetration to Fresnel radius is greatest — that is your critical obstacle. The path profile chart in this calculator reveals that worst-case point visually.
For paths longer than about 30 km on VHF, the required Fresnel clearance can easily exceed 100 m, making tower height alone insufficient. In these cases, consider a repeater or passive repeater (reflector), an APRS digipeater, or an active relay node. On microwave bands (3 GHz and above) the narrower Fresnel zone makes long-distance terrestrial paths more practical with modest antenna heights, but multipath from reflective surfaces (water, wet ground, metal roofs) becomes a new concern and path diversity or polarization switching may be needed.
Frequently Asked Questions
What is a Fresnel zone?
Fresnel zones are concentric ellipsoidal regions around the direct line-of-sight path between TX and RX. The 1st zone defines the volume where reflected or diffracted waves arrive within half a wavelength phase difference from the direct wave; obstacles within it cause signal loss. The formula for the first zone radius at any point is r₁ = √(λ × d₁ × d₂ / (d₁ + d₂)), where d₁ and d₂ are distances from the obstacle to each end.
Why is 60% Fresnel zone clearance the rule of thumb?
Theoretical free-space propagation is maintained when the 1st Fresnel zone is completely unobstructed. However, maintaining at least 60% clearance reduces the additional path loss to less than 0.5 dB in practice, which is acceptable for most links. Full 100% clearance is ideal but often impossible in hilly terrain; engineers use the 60% standard as the practical minimum.
Where is the Fresnel zone largest along the path?
The 1st Fresnel zone radius is maximum at the midpoint of the path. This is why mid-path obstacles are the most critical. For a 50 km path at 146 MHz, the mid-path radius can be tens of meters, while near the antennas it shrinks to zero.
Does Fresnel zone matter for short VHF/UHF paths?
Yes — even on short urban links at 2.4 GHz or 5.8 GHz, a building at 60% clearance may only need 2–3 m of additional height clearance, but missing it can cost 6+ dB. On longer HF or VHF paths the zone can be hundreds of meters wide, making terrain obstruction the dominant link budget factor.
What happens when an obstacle enters the 2nd Fresnel zone?
The 2nd Fresnel zone contains reflected waves that arrive in phase opposition with the direct wave. If an obstacle diffracts energy back into the path from the 2nd zone, it can actually cause a small gain relative to the obstructed 1st zone. Beyond that, each successive zone alternates constructive and destructive interference, but the contribution diminishes rapidly.
How do I use this for path planning on a digital link?
Combine this calculator with a terrain profile (from topo maps or tools like SPLAT!). Identify the highest terrain point relative to the line-of-sight and input its distance from TX as the obstacle position. If the required 60% clearance height exceeds the actual antenna height above that terrain, you need higher masts, a repeater, or an alternative path.
Sources and References
- ARRL Antenna Book, 25th Edition — Chapter on VHF/UHF and Microwave Antenna Systems, Fresnel zone clearance guidelines
- ITU-R Recommendation P.526-15 (2019) — Propagation by diffraction, Fresnel-Kirchhoff diffraction theory and knife-edge loss models
- Pozar, D.M., Microwave Engineering, 4th Edition (Wiley, 2011) — Chapter 1: Electromagnetic Theory, propagation and Fresnel zones
- Balanis, C.A., Antenna Theory: Analysis and Design, 4th Edition (Wiley, 2016) — Aperture antennas and Huygens principle underlying Fresnel zone analysis
- Seybold, J.S., Introduction to RF Propagation (Wiley, 2005) — Chapter 5: Diffraction and Fresnel zone obstruction loss