HuntsvilleEngineers mark

Fresnel Zone Clearance

First-zone radius at mid-path and the 60% clearance a microwave link actually needs.

Inputr₁ = 17.32·√(d/(4f)) at mid-path, d in km, f in GHz, r in m

Your recent runs (stored only in your browser)

No calculations yet — results land here so you can compare runs.

The engineering

Line of sight is not enough — radio needs an ellipsoid of clear air around the ray, because energy arriving via paths up to half a wavelength longer still adds constructively. Graze that ellipsoid with a treetop or roofline and the link fades even though you can see the far tower. The rule of practice: keep 60% of the first zone clear and you're within ~1 dB of true free space.

The zone is fattest at mid-path (this card's number) and lower frequencies dig deeper: a 10 km link needs 17.7 m of half-width at 2.4 GHz but 30 m at 900 MHz-ish frequencies. Remember trees grow, and over long paths add earth bulge and refraction (effective 4/3 earth radius) on top of this geometry.

Where this math comes from

Augustin-Jean Fresnel drew these zones in his 1818 memoir on diffraction — the wave-theory tour de force whose oddest prediction (a bright spot behind an opaque disc) Arago promptly confirmed, converting a skeptical Academy. The zones were pure optics for a century before radio inherited them.

André Clavier's 1931 microwave hop across the English Channel and the postwar AT&T TD-2 relay network (1950, New York to Chicago and onward) turned Fresnel's construction into tower-height budgets — every microwave path profile since is this card plus terrain data.

  1. 1818Augustin-Jean FresnelZone construction in the prize memoir on diffraction.
  2. 1931André Clavier (ITT/LCT)First commercial microwave link, Calais–Dover — clearance becomes engineering.
  3. 1950AT&TTD-2 transcontinental microwave relay; path profiling standardized.

See the full timeline of the math behind every calculator →

Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.