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Fresnel Zone Calculator

This Fresnel Zone and Antenna Height calculator helps you determine if you have “radio line of sight” between two distant points, or alternatively, how high you need to elevate either antenna to clear an obstruction.  The calculator takes into account the earth’s curvature and effects from refraction in the atmosphere.

Following the Fresnel Zone calculator you can find a short tutorial of RF propagation effects and the requirement for Fresnel zone clearance.  If you have any comments or suggestions for improving this calculator send us a message.

Fresnel Zone Clearance and Antenna Height Calculator

Input
MHz

(typical 1.33)

%

(typical 60%)

miles

ft
ft

miles
miles
ft
Units:
Output

5265 miles

Equal Antenna Height Solution:

at midpoint:

61.8 ft

Height of both antennas
for FZ clearance:

112.0 ft

Minimum Clearance Point:

Distance from site 1:

11.2 miles

Clearance between Earth and FZ:

7 ft

Clearance at Point P:

53.5 ft

Clearance between obstruction and FZ:

39 ft

Fresnel Zone Clearance and Antenna Height Calculator

At UHF and microwave frequencies, when you deploy an RF link between two distant sites you need to make sure you have “line of sight” between the two antennas.  But at these frequencies “line of sight” does not simply mean that from one site you can “see” the other.  When your distance exceeds, say, 5 miles (8 km), you need to take into account the following factors:
• The curvature of the earth.
• Fresnel Zone clearance.
• Atmospheric refraction.
The figure below illustrates these concepts with an exaggerated representation of a long link.  The following sections describe these effects.

Fresnel Zone Definition

The Fresnel zone is a long ellipsoid that stretches between the two antennas.  The first Fresnel zone is such that the difference between the direct path (AB in the figure below) and an indirect path that touches a single point on the border of the Fresnel zone (ACB) is half the wavelength.

If a significant portion of the Fresnel zone is obstructed the receive-signal-strength at the receiving antenna can be greatly attenuated.  A rule of thumb is that you need at least 60% of the first Fresnel zone clear of any obstructions in order for the radio wave propagation to behave as if it is in “free space”.  “60% of the first Fresnel zone” means a narrower ellipsoid with a radius that is 60% of the radius of this first Fresnel zone.

Even though at 2.4 GHz half of the wavelength is only 2.4 inches (6.2 cm), at long distances the radius of this ellipsoid can be quite large.  For example, with a link distance of 31 miles (50 km) the radius of this (60%) ellipsoid at the mid-point is 77 ft (23 meters).  You can use the calculator to compute this radius at any point in between the two antennas.  You may also change the percent value of the first Fresnel zone you wish to clear.

Atmospheric Refraction

Under normal atmospheric conditions radio waves do not propagate in a straight line, they actually bend slightly downward.  This is due to “refraction” in the atmosphere which affects radio waves propagating horizontally.  To take this downward bending into account, we perform all the path calculations using a larger value for the earth radius, such that we can then consider the radio waves as propagating in a straight line.

In the Fresnel zone calculator you can change the earth radius multiplying factor (the “k factor”) to take into account different atmospheric conditions.  Under normal conditions the “k factor” is 4/3.  However unusual weather conditions can cause significant changes to the refraction profile.  For a high reliability link you may want to use a lower value for the k factor.

Equal Antenna Height Solution

For any given distance the Fresnel zone calculator displays the antenna heights (same at both ends) such that the Fresnel zone just clears the earth surface as shown in the figure below.

Different antenna heights

It is unusual that you would have both antennas at the same height, so the calculator lets you enter different heights for the two end points (all heights are above sea-level; see “h1” and “h2” in the figure at the top).

The calculator computes the “minimum clearance point” which is the point in the path where the Fresnel zone is closest to the earth sea-level.  It displays both the distance from site 1 and the clearance between the earth sea-level and the low boundary of the Fresnel zone.  A negative clearance means the Fresnel zone overlaps with the earth profile.

Clearing an obstruction

The calculator allows you to quickly determine whether you have enough clearance above a particular obstruction in the RF path, or alternatively, how high you need to elevate your antennas to clear the obstruction.

For each potential obstruction in the path you need to know its distance from one of your end points and the height of the obstruction above sea-level. Drawing the path in “Google Earth ” is a quick way of identifying buildings or structures that lay in the direct path and finding their distance from the end points.  You may need to use a topographic map, draw the line between the end points, and create an accurate terrain profile.  If there are buildings or trees in the path you need to determine or estimate their height above the ground, and add it to the terrain elevation at those points.

For each of these potential obstruction points, enter its distance from site 1 and the height of the obstruction above sea level in the bottom left input “spinners” of the calculator.   On the right hand side the calculator displays the vertical separation between the top of the obstruction and the bottom of the Fresnel Zone.  If this value is negative you can use the antenna height spinners to increase the height of one or both antennas until that clearance becomes greater than zero.