Parabolic Antenna Pattern Calculator and Formula

A parabolic antenna pattern calculator estimates a dish’s beamwidth and the signal level away from its main pointing direction. Enter the operating frequency and dish diameter to calculate an approximate half-power beamwidth; the result is a useful planning estimate, not a full measured radiation pattern.

Formula

This calculator uses the common engineering approximation for the full half-power beamwidth of a circular parabolic reflector:

θ ≈ 70 λ / D, where θ is beamwidth in degrees, λ is wavelength in the same length unit as D, and D is the reflector diameter.

It calculates wavelength from frequency using λ = c / f. In the calculator’s units, this is approximately λ in millimetres = 300 / f in gigahertz. The expression is therefore θ ≈ 70 × [300 / (f × 1000)] / D, with D in metres. The factor 1000 converts wavelength from millimetres to metres. The second output repeats the calculated beamwidth as the half-power beamwidth, the standard interpretation of this approximation.

The estimate assumes a properly illuminated circular dish and a conventional aperture-efficiency profile. Real beamwidth depends on feed illumination, dish shape, blockage, surface accuracy, and the measurement convention. It is not a prediction of every point in the antenna’s pattern.

Worked Example

Using the calculator’s defaults, frequency is 12 GHz and dish diameter is 0.6 m.

1. Calculate wavelength: λ ≈ 300 / 12 = 25 mm.
2. Convert wavelength to metres: 25 / 1000 = 0.025 m.
3. Apply the approximation: θ ≈ 70 × 0.025 / 0.6 = 2.9167 degrees.
4. Rounded to two decimal places, the approximate beamwidth is 2.92 degrees.

This is the full angular width between the points where the main lobe falls to half its peak power, also called the −3 dB points. It is not a 2.92-degree radius on each side of the center; for a roughly symmetric beam, the half-width is about 1.46 degrees.

How a Parabolic Antenna Pattern Works

A parabolic reflector gathers incoming radio waves and directs them toward a feed, or sends waves from the feed into a concentrated direction. The main lobe points along the dish axis. A narrower main lobe means the antenna is more directional and requires more accurate alignment.

The calculator estimates only the main-lobe width. A complete radiation pattern also includes sidelobes, which are smaller lobes away from the main direction, and may include a back lobe. Their levels and positions depend on the reflector and feed design. Beamwidth alone cannot describe sidelobe suppression, polarization, gain, or performance across a frequency band.

When to Use the Estimate

Beamwidth is useful for judging how carefully a dish must be aimed, comparing reflector sizes at the same frequency, and anticipating how much of the sky or a target area the main beam covers. For example, doubling dish diameter at the same frequency halves the estimated beamwidth. Doubling frequency while keeping diameter fixed also halves it, because the wavelength is halved.

• Aiming: A narrow beam makes small pointing errors more significant.
• Coverage: A wider beam covers more angular area, but generally concentrates less energy in the desired direction.
• Comparisons: Use the same beamwidth convention and consistent units when comparing antennas.

For a rough linear footprint at a known distance, multiply the angular width in radians by the distance. Convert degrees to radians by multiplying by π/180. This gives an approximate full-width footprint near the boresight; it does not account for terrain, obstructions, or propagation effects.

Choosing Inputs and Understanding Accuracy

Use the actual reflector diameter, not the feed diameter or the dish’s focal length. The diameter should be the width across the reflecting aperture. Enter the operating frequency in gigahertz; for a system that operates across a band, calculate at the frequency relevant to the link or compare the band’s endpoints.

The displayed estimate is most useful for preliminary design. Manufacturers may specify beamwidth using a different factor, a measured pattern, or a particular plane. A dish can have different pattern widths in its principal planes if it is not perfectly circular or has construction irregularities. For a precise link budget or pointing requirement, use a measured antenna pattern or a specification for the exact antenna and frequency.

Dish efficiency affects gain more directly than this simplified beamwidth calculation. An often-used gain estimate is G ≈ η(πD/λ)², where η is aperture efficiency. Since efficiency varies by design and frequency, do not infer exact gain from beamwidth alone. A larger reflector often gives both higher gain and narrower beamwidth, but the calculator does not quantify gain.

Common Mistakes and Limits

• Mixing units: The calculator expects GHz and metres. If a diameter is given in feet, convert it first: 1 ft = 0.3048 m. If using the formula directly, λ and D must use the same units.
• Treating the estimate as exact: The factor 70 is an approximation. Alternate practical rules use different factors, depending on illumination and the intended beamwidth definition.
• Confusing beamwidth with pointing tolerance: The half-power width is not a guaranteed alignment tolerance. Signal loss depends on the actual pattern and how far the antenna is mispointed.
• Ignoring physical condition: A warped, obstructed, or poorly illuminated reflector can have a pattern unlike the idealized estimate.

The calculation does not account for atmospheric absorption, rain fade, cable loss, receiver sensitivity, or interference. Those factors matter to a real communications link but are separate from the geometric beamwidth estimate.

Frequently Asked Questions

What does parabolic antenna beamwidth mean?
It usually means the full angular separation between the two directions where the main beam’s power is half its peak value, or 3 dB below the peak. It is commonly reported in degrees.

Does a bigger dish have a narrower beam?
Yes, at a fixed frequency the approximate beamwidth is inversely proportional to dish diameter. A dish twice as wide has about half the estimated beamwidth under the same assumptions.

Does higher frequency make a dish more directional?
For the same diameter, higher frequency means shorter wavelength and a narrower estimated beam. The formula does not guarantee better real-world reception, since losses and antenna performance also vary with frequency.

Is beamwidth the same as antenna gain?
No. Beamwidth describes the angular spread of the main lobe. Gain describes how strongly an antenna concentrates power in a direction compared with a reference antenna; gain also depends on aperture efficiency and other design details.

Can this calculator give the full radiation pattern?
No. It estimates the main-lobe half-power width only. A full pattern, including sidelobes and back-lobe levels, requires antenna-specific design data or measurements.

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in f | Frequency | GHz | 12 | 0
in d | Dish diameter | m | 0.6 | 0
out bw | Approximate beamwidth | degrees | 70 * (300 / (f * 1000)) / d | 2
out hpbw | Half-power beamwidth | degrees | bw | 2