RF Wavelength, Antenna & Path Loss Calculator
Wavelengths, antenna lengths, link budgets and line-of-sight clearance in one place.
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About the RF Wavelength, Antenna & Path Loss Calculator
Four radio calculations that belong together. Wavelength converts between frequency, wavelength and period, in vacuum or air or in a cable with its velocity factor, with the fractions of a wavelength you cut stubs and elements to. Antenna lengths gives the length of a half-wave dipole and each leg, a quarter-wave vertical, a 5/8-wave vertical and λ/4 and λ/2 coax sections, with the end-effect shortening that makes real elements a little shorter than half a wave.
Path loss & link budget works out the free-space path loss, the EIRP, the power at the receiver and the fade margin against its sensitivity, and how far the link would reach with nothing in the way. Fresnel zone & horizon gives the radius of the first Fresnel zone at any point of a path, the 60 % clearance to keep, the Earth bulge and the radio horizon of each antenna.
Without a pass, the free preview runs on your own values: it shows the notes that apply and the labels of the first rows of each table, with the wavelength, element length, received power or Fresnel radius, every other figure and the working hidden; the full result, Copy result and the CSV come with a Pro pass.
How to use it
- Choose what to work out: Wavelength, Antenna lengths, Path loss & link budget or Fresnel zone & horizon.
- Type the frequency (or, for the wavelength, a wavelength or a period) and pick the medium or the velocity factor of your cable.
- For a link, enter the distance, the transmitter power, both antenna gains, the cable losses and the receiver’s sensitivity; for a Fresnel zone, the path length, where the obstacle is and the antenna heights.
- Read the result, the table and the working, then copy the result or download it as CSV — with a pass, or after unlocking this result.
Examples
146 MHz, velocity factor 1
λ = 2.0534 m, period 6.849 ns
2.4 GHz
λ = 12.49 cm
100 MHz, velocity factor 0.66
λ = 1.9786 m (2.9979 m in vacuum)
7.1 MHz, shortening factor 0.95
20.06 m (65.8 ft) in total, 10.03 m per leg; the 468 ÷ f rule gives 65.9 ft
146 MHz
Quarter-wave vertical 48.77 cm (19.2 in); a λ/4 section of solid-PE coax is 33.88 cm
20 dBm, 2 dBi antennas, 1 dB cable at each end, −90 dBm receiver
Path loss 100.05 dB, EIRP 21 dBm, received −78.05 dBm, margin 11.95 dB, about 3.96 km at 0 dB margin
10 km path, obstacle at the middle
r₁ = 11.37 m, keep 6.82 m clear, Earth bulge 1.47 m (k = 4/3)
Wavelength and velocity factor
λ = v ÷ f with v = VF × c, where c = 299,792,458 m/s exactly (the SI definition) and VF is the velocity factor: 1 in vacuum and very nearly 1 in air, 1/√εr in a cable whose dielectric has the relative permittivity εr. Solid polyethylene (εr ≈ 2.3) gives about 0.66, PTFE (εr ≈ 2.1) about 0.70 and foamed dielectrics 0.8 to 0.88; your cable’s datasheet gives its exact figure. The period is T = 1 ÷ f.
Antenna element lengths
- Half-wave dipole: L = k × λ₀ ÷ 2. The shortening factor k is about 0.95 for wire, which gives the familiar 468 ÷ f(MHz) feet (143 ÷ f metres); very thin wire needs about 0.98 and thick tubing about 0.94.
- Quarter-wave vertical (ground plane): L = k × λ₀ ÷ 4.
- 5/8-wave vertical: 0.625 × λ₀ × k as a starting point; it needs a matching coil at its base, which sets the final length.
- Coax sections: λ/4 = VF × λ₀ ÷ 4 for a quarter-wave transformer or stub, λ/2 = VF × λ₀ ÷ 2 to repeat an impedance.
An isolated half-wave dipole, far from the ground and other objects, has a feedpoint resistance of about 73 Ω, and a quarter-wave vertical over a perfect ground about 36 Ω (dipole antenna). Cut a little long and trim while you measure the SWR.
Free-space path loss and the link budget
- Path loss: L = 20·log₁₀(4π·d ÷ λ) = 20·log₁₀(4π·d·f ÷ c), which is 32.45 + 20·log₁₀ f + 20·log₁₀ d with f in MHz and d in km (Recommendation ITU-R P.525 writes the constant as 32.4).
- EIRP = transmitter power + transmit antenna gain − transmit cable loss (dBm, dBi and dB).
- Received power = EIRP − path loss − other losses + receive antenna gain − receive cable loss.
- Fade margin = received power − receiver sensitivity. Every doubling of the distance adds 6.02 dB of free-space loss, so the range at 0 dB margin is d × 10^(margin/20).
Fresnel zone, Earth bulge and radio horizon
- First Fresnel zone: r₁ = √(λ·d₁·d₂ ÷ d) at distances d₁ and d₂ from the two ends of a path of length d, widest at the middle: ½·√(λ·d). Recommendation ITU-R P.526 writes it as 550·√(d₁·d₂ ÷ (d·f)) metres with distances in km and f in MHz. Keep at least 60 % of it clear.
- Earth bulge: b = d₁·d₂ ÷ (2·k·a) with a = 6,371 km; the effective Earth radius factor k is 4/3 in a standard atmosphere.
- Radio horizon: d_h = √(2·k·a·h) for an antenna h above the ground, about 4.12·√h km with h in metres for k = 4/3. Two antennas can see each other up to the sum of their horizons.
Limitations
- The path loss is the free-space value between antennas in each other’s far field. Terrain, buildings, the ground, foliage, rain and multipath add loss on real paths; use a propagation model for those.
- Antenna lengths are starting points: height, nearby objects, insulation and the feedline change the resonant length, so trim while measuring SWR.
- The Fresnel and horizon figures assume a smooth Earth with a constant k; real refraction varies with the weather.
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Frequently asked questions
What do I get without a pass?
Without a pass, RF Wavelength, Antenna & Path Loss Calculator shows the names of each table’s first rows (up to 3), with the wavelength, length, power or Fresnel radius, the working and every other figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I convert frequency to wavelength?
Divide the speed of light by the frequency: λ = 299,792,458 ÷ f. For quick sums, λ(m) ≈ 300 ÷ f(MHz): 146 MHz is 2.05 m and 2.4 GHz is 12.5 cm. In a cable, multiply by its velocity factor.
How long should a half-wave dipole be?
About 468 ÷ f(MHz) feet, or 143 ÷ f(MHz) metres, from tip to tip, which is 95 % of a free-space half wavelength. For 7.1 MHz that is about 65.9 ft (20.06 m), half of it in each leg. Cut it slightly long and trim it for the lowest SWR.
What is free-space path loss?
The loss between two isotropic antennas with nothing in between: 20·log₁₀(4πd ÷ λ). At 2.4 GHz it is 100 dB over 1 km, and every doubling of the distance or the frequency adds 6 dB.
What fade margin do I need?
The difference between the received power and the receiver’s sensitivity. The free-space loss is the best case, so links are designed with room to spare for fading, weather, obstructions and misalignment; the calculator warns below 10 dB.
Why must the Fresnel zone be clear if I can see the other antenna?
Radio energy travels in a wide ellipsoid around the line of sight, not just along it. Obstacles inside the first Fresnel zone diffract and reflect part of it and add loss, so links keep at least 60 % of its radius clear, plus the Earth bulge on long paths.