Fresnel Zone Calculator — Radius, Clearance & Antenna Height for Wireless Links

What is the Fresnel zone?

The Fresnel zone calculator allows you to determine the length of the radius at any point of the Fresnel space. With it, you can ensure strong signal transmission between your antennas. In this article we cover everything you need to know about the topic — what the Fresnel zone is, the formulas you need to calculate Fresnel zones, why they matter, and how to choose your antenna height to avoid signal obstruction.

In wireless communication there is a 3D elliptical region between the transmitter antenna and the receiver antenna. This region is determined by the distance between the antennas and the frequency of the wireless wave. It is called the Fresnel zone.

In the Fresnel zone, the longest axis of the ellipsoid is the line-of-sight path. Keeping it free of constructions in the region between the antennas is critical because obstructions cause signal loss. However, even obstructions that do not cross the line-of-sight path can cause signal loss. How is that possible?

Wireless antennas send waves in different directions. Some waves arrive directly at the receiver — the direct beam — and others arrive after reflecting off other surfaces — the indirect beams. Indirect beams travel a longer path, so their phase angle is shifted compared with the direct beam. Whenever the phase angle shifts by one-half wavelength, you get destructive interference, meaning the signals cancel.

To avoid the harmful effects of indirect beams, you should keep at least 60% of the 1st Fresnel zone free of obstructions. 80% is the recommended value. Subsequent Fresnel zones (2nd, 3rd, …) are also relevant but not as critical as the first one.

Fresnel zone formulas

The formula for the radius of the n-th Fresnel zone is:

r_n = √(n × λ × d1 × d2 / (d1 + d2))

where:

• λ is the wavelength of the wireless beam transmitted by the antenna;
• d1 is the distance from the first antenna to the point;
• d2 is the distance from the second antenna to the point; and
• r_n is the radius of the n-th zone at that point.

To get the longest Fresnel zone radius (r_n,max) recall that an ellipsoid is widest at its center, i.e., when d1 = d2 = D / 2. The formula then simplifies to:

r_n,max = √(n × λ × D / 4)

First Fresnel zone formulas

To determine the radius at any point in the first Fresnel zone (n = 1):

r = √(λ × d1 × d2 / (d1 + d2))

And for the 1st Fresnel zone longest radius:

r_1,max = √(λ × D / 4)

Using the wavelength formula (λ = c / f), this becomes:

r_1,max = √(c × D / (4 × f))

where f is the wireless beam frequency. Wireless waves travel at the speed of light (they are electromagnetic waves), so c = 300,000 km/s. If you input D and f in kilometers and GHz respectively, you obtain:

r_1,max = 17.32 × √(D / (4 × f)), expressed in meters.

Another way of expressing this equation is:

r_1,max = 8.66 × √(D / f), expressed in meters.

Why is the Fresnel zone important?

If too much of the first Fresnel zone is blocked — by terrain, buildings, or trees — the link budget degrades and the connection becomes unreliable, even when the two antennas can "see" each other. Planning a link so that at least 60% (ideally 80%) of the first zone stays clear is essential for stable Wi-Fi bridges, point-to-point microwave links, and long-range LoRa or radio communication.

How to calculate the Fresnel zone? Example

Suppose two antennas are 1 km apart and the point of interest is exactly in the middle (d1 = d2 = 500 m), operating at 2.4 GHz.

1. Wavelength: λ = c / f = 300,000,000 / 2,400,000,000 ≈ 0.125 m.
2. First zone radius at the midpoint: r = √(0.125 × 500 × 500 / 1000) ≈ 3.95 m.
3. Recommended 80% clearance: 0.8 × 3.95 ≈ 3.16 m.
4. Minimum 60% clearance: 0.6 × 3.95 ≈ 2.37 m.

So at mid-span you would want to keep roughly a 3.16 m radius around the line of sight free of obstacles.

How to use our Fresnel zone calculator for antenna height selection?

Enter the operating frequency, the two distances d1 and d2 from each antenna to the point you are checking (usually the highest obstacle along the path), and the zone number (use 1 for the most important zone). The calculator returns the zone radius at that point, the maximum radius at mid-span, and the 60% and 80% clearance values. Make sure your antennas are mounted high enough that the obstacle stays below the 80% clearance radius. Both the metric (m, km) and American/imperial (ft, mi) unit systems are supported.

FAQs

What percentage of the first Fresnel zone must be clear?

At least 60% must be unobstructed for an acceptable link; 80% is the recommended target for a reliable, low-loss connection.

Where is the Fresnel zone widest?

The Fresnel zone is widest at the midpoint between the two antennas, where d1 = d2 = D / 2.

Does a higher frequency make the Fresnel zone larger or smaller?

Higher frequency means a shorter wavelength, which makes the Fresnel zone radius smaller. Lower frequencies produce larger zones that require more clearance.

What are higher-order Fresnel zones?

Beyond the first zone there are concentric elliptical zones (2nd, 3rd, …) where reflected signals alternately add to or cancel the direct signal. They matter less than the first zone but can still influence the received signal.