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Fresnel zone calculator

What the Fresnel zone is

The Fresnel zone is an ellipsoid around the straight line between transmitter and receiver, within which radio waves travel without appreciable loss. Obstacles inside it can attenuate or distort the signal.

rd 10 кмan obstacle inside the zone weakens the signal noticeably
r — radius of the first Fresnel zone at mid-path, d — distance between the antennas
Standard frequencies
Frequency (MHz)
Distance
Units of the result
Result
Radius of the 1st Fresnel zone (100%)
Radius of the 1st Fresnel zone (80%)

📐 The formulas​

The calculator uses the formula taken from professional planning software:

The main formula​

Radius of the first Fresnel zone:

R = 17.3 × √(d / (f/1000 × 4))

80 % of the Fresnel zone (the critical zone):

R₈₀ = 0.8 × R

Symbols:​

  • R — Fresnel zone radius [m]
  • d — distance between transmitter and receiver [km]
  • f — signal frequency [MHz]

The theory behind it​

The full theoretical formula for the Fresnel zone:

R = √(λ × d₁ × d₂ / (d₁ + d₂))

where:

  • λ — wavelength [m]
  • d₁, d₂ — distances from transmitter and receiver to the obstacle [m]

At the midpoint of the path (d₁ = d₂ = d/2) the formula simplifies to the one used in the calculator.

Where this calculator stops:
  • Distance: up to 1000 km
  • Frequency: from 1 MHz to 10 GHz
  • Units: results in metres, distance in kilometres
  • The zone is worked out for the midpoint of the path
  • Terrain and the curvature of the Earth are not accounted for
  • The results are approximate and assume ideal propagation

🎯 In practice​

Reading the results:​

100 % of the Fresnel zone:

  • The full radius of the first Fresnel zone
  • Obstacles inside it can affect the signal
  • Best kept clear

80 % of the Fresnel zone (the critical zone):

  • The most important region to keep clear
  • Obstacles here will certainly degrade the signal
  • It sets the minimum antenna height

Where it is used:​

  1. Planning WiFi networks

    • Working out the best antenna height
    • Judging the effect of buildings and other obstacles

  2. Amateur radio

    • Planning long-distance links
    • Choosing where to put the antennas

  3. Professional radio networks

    • Planning operator networks
    • Working out base station coverage

  4. Satellite communications

    • Planning ground stations
    • Judging the effect of terrain

Recommendations:​

  • For a reliable link: keep 80 % of the Fresnel zone clear
  • For the best link: keep 100 % of it clear
  • At higher frequencies: the zone is smaller but more critical
  • Over long distances: allow for the curvature of the Earth and refraction
Practical advice:
  1. Antenna height: raise the antennas enough to clear 80 % of the Fresnel zone
  2. Frequency: at higher frequencies (5–6 GHz) the zone is smaller, but obstacles matter more
  3. Distance: the zone grows as the distance grows
  4. Planning: use topographic maps for accurate planning
  5. Testing: always check theoretical figures against real measurements

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Fresnel zone calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/other/fresnel (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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