Fresnel Zone - First-Zone Radius, Clearance, FSPL

A Fresnel zone calculator works out the elliptical volume of space around the line of sight between two radio antennas where the signal travels. Enter the link distance, the carrier frequency, and a point along the path, and the calculator reports the first Fresnel zone radius at that point, the 60% clearance target above any obstruction, and the free-space path loss you should expect. Point-to-point Wi-Fi bridges, microwave backhaul links, amateur radio paths, and drone control links share the same Fresnel geometry.

• • Point-to-point Wi-Fi bridges: Plan 2.4 GHz and 5 GHz outdoor bridges between buildings by checking the Fresnel radius at the tallest obstruction.
• • Microwave backhaul links: Estimate the first Fresnel zone radius and FSPL for licensed links at 5, 6, 11, or 23 GHz.
• • Amateur radio and repeater paths: Check VHF/UHF coverage along ridges where the Fresnel zone is partially blocked.
• • Drone and FPV links: Estimate Fresnel clearance along a long-range drone link at 900 MHz, 2.4 GHz, or 5.8 GHz.

Fresnel zones come from constructive interference. The first zone is the set of points where the indirect path differs from the direct line of sight by less than half a wavelength, so anything solid inside that volume absorbs energy.

If the Fresnel radius looks larger than expected, the cause is usually a long wavelength rather than a long link, so the Frequency of Light Calculator is the next step to convert a 2.4 GHz carrier into the same physical wavelength that defines the first zone.

The Fresnel zone calculator uses one geometric formula and one link-budget formula. The geometric formula gives the radius of the first Fresnel zone at any point along the path. The link-budget formula converts the link distance and carrier frequency into free-space path loss in dB.

• r: Radius of the first Fresnel zone at the chosen point, in metres.
• λ (lambda): Wavelength of the carrier in metres, computed as c / f with c = 299,792,458 m/s.
• d1, d2: Distances from the point of interest to antenna 1 and antenna 2 in metres; d1 + d2 = D.
• D: Total link distance, kilometres in the FSPL formula and metres inside the geometric formula.
• f: Carrier frequency in megahertz for the FSPL formula.

When the point of interest is the path midpoint, d1 = d2 = D/2 and the formula simplifies to r = (1/2)·sqrt(λ·D). The 32.44 dB constant folds in 20·log10(4π / c) once D is in kilometres and f is in MHz, so the FSPL output is the standard Friis free-space equation used in link-budget worksheets.

According to the BIPM SI Brochure, the speed of light in vacuum is exactly 299,792,458 m/s by the SI definition of the metre. According to ITU-R P.526, the radius of the n-th Fresnel zone at a distance d1 from one end and d2 from the other is r_n = sqrt(n · λ · d1 · d2 / (d1 + d2)), and roughly 60% clearance of the first Fresnel zone is the practical minimum for terrestrial radio links.

When the wavelength used inside the Fresnel formula needs to be turned back into a wave picture, the Harmonic Wave Equation Calculator converts the same carrier frequency into wavelength, period, and the full wave number.

Four ideas frame every link-planning decision: what a Fresnel zone is, how its radius changes along the path, why roughly 60% clearance is the practical target, and how free-space path loss sets the floor on the link budget.

When a Fresnel-zone study shows that grazing terrain is the dominant loss, the Brewster Angle Calculator explains how reflection coefficients change with incidence angle at the same frequency.

Enter the link distance, the carrier frequency, the point of interest along the path, and any actual clearance. The Fresnel zone calculator then outputs the radius, the 60% clearance target, the free-space path loss, and the obstruction percentage.

1. 1 Enter the total link distance: Type the straight-line distance between the two antennas in kilometres. Survey maps, GPS, or a laser rangefinder work. For a 2 km link, type 2.
2. 2 Enter the carrier frequency: Type the carrier frequency in MHz. Common values are 900, 2400, 5000, 5800, or 24000 MHz.
3. 3 Enter the point of interest: Type the distance from antenna 1 to the point of interest in kilometres. Leave at half of the total distance for the midpoint.
4. 4 Add the actual clearance (optional): Type a survey height for the terrain or obstruction at the point of interest in metres. Leave at 0 for geometry and FSPL only.
5. 5 Read the Fresnel radius and clearance: The primary readout is the first Fresnel zone radius. The 60% clearance target is shown next, so it can be compared with the actual clearance above.
6. 6 Read the FSPL and obstruction percentage: Use the free-space path loss as the link-budget floor. The obstruction percentage quantifies how much of the Fresnel zone is blocked.

For a 2.4 GHz bridge across 2 km with 3 m of clearance at the midpoint, the Fresnel radius is 7.903 m, the 60% target is 4.742 m, the FSPL is 106.06 dB, and the obstruction percentage is 62.0%.

After the carrier is fixed, the Frequency Bandwidth Calculator sizes the channel bandwidth around that carrier.

The Fresnel zone calculator compresses four textbook formulas into one read, so link planning no longer needs a chart and an FSPL table open at the same time.

• • One panel, four answers: Enter the link distance, carrier frequency, and point of interest once, and read the Fresnel radius, the 60% clearance target, the FSPL, and the obstruction percentage together.
• • Built-in unit safety: Distance and frequency are entered in km and MHz, the units used in link budgets, and the calculator converts internally.
• • Off-midpoint evaluation: The distance-from-antenna-1 input lets the calculator evaluate any point along the path, not just the midpoint, which is useful when the worst obstruction sits closer to one end.
• • Link-budget floor: The FSPL output matches link-budget worksheets, so it can be pasted into a spreadsheet without unit conversion.
• • Obstruction readout: When actual clearance is supplied, the obstruction percentage quantifies how much of the Fresnel zone is blocked.

When the link budget needs an angular frequency in radians per second instead of Hz, the Angular Frequency Calculator converts the same carrier into the ω used in wave-propagation formulas.

The Fresnel geometry is exact, so surprising answers come from the input side or the assumptions baked into the FSPL formula.

• • The calculator assumes a perfectly flat, uniform path. Real terrain and vegetation add attenuation beyond the FSPL number.
• • The 60% clearance rule is a planning rule of thumb. Heavy vegetation or wet foliage can cause additional loss even at 60% clearance, especially above 5 GHz.
• • Free-space path loss assumes isotropic antennas in vacuum. Real antennas have gain, and polarization mismatch adds further loss that FSPL does not capture.

According to ITU-R P.525, the free-space attenuation between isotropic antennas is A_fs_dB = 20·log10(d) + 20·log10(f) + 20·log10(4π/c) where d is in metres and f is in hertz, which simplifies to 32.44 + 20·log10(d_km) + 20·log10(f_MHz) for the units used in the calculator.

Once the FSPL floor is known, the Attenuation Calculator folds the extra dB per metre from foliage, walls, or atmospheric layers into the same dB scale so the link budget can add those losses on top of the free-space number.