Path Parameters
Calculated Results
Line of Sight Distance ($$d_{los}$$): --
Radio Horizon ($$d_r$$): --
1st Fresnel Zone Radius: --
Fresnel Clearance at Midpoint: --
Drag the slider to adjust the obstacle's height.
Obstacle Height: 0mHow It Works: The Formulas Behind LOS
Visual Line of Sight
The maximum distance to the horizon from an antenna at a given height (h) is calculated by a simple geometric formula. This assumes a flat Earth and no atmospheric effects.
$$d_{los} = 3.57\sqrt{h}$$
(where $$d_{los}$$is in km and $$h$$ is in meters)
This is the geometric or "visual" horizon, the furthest point you could theoretically see from the antenna.
Radio Horizon
Because of atmospheric refraction, radio waves bend slightly with the Earth's curvature. This extends the effective range, a phenomenon represented by the k-factor (approximately 4/3). The radio horizon is typically longer than the visual horizon.
$$d_r=4.12\sqrt{h}$$
(where $$d_r$$is in km and $$h$$ is in meters)
This formula gives a more realistic maximum range for RF signals under normal atmospheric conditions.
The Fresnel Zone
For a reliable wireless link, a clear line of sight is not enough. The signal requires a clear, ellipsoidal area around the direct path, known as the Fresnel Zone. Obstructions within this zone can cause signal attenuation or cancellation. The radius (r) of the first Fresnel zone at the midpoint of a link is:
$$r = 17.32\sqrt{\frac{d}{4f}}$$
(where $$r$$is in meters, $$d$$is in km, and $$f$$ is in GHz)
Most experts recommend at least 60% clearance of the first Fresnel Zone for a strong, reliable link.
