---
title: What's the Beam for that Gain?
description: How do aperture, gain and beamwidth relate in antenna systems?  This physics explainer shows the maths and the graphs
---

[RFolutionaries ](https://www.cyntony.com/blog)

# [What's the Beam for that Gain?](https://www.cyntony.com/blog/whats-the-beam-for-that-gain)

 Written by [David A Moschella](https://www.cyntony.com/blog/author/david-a-moschella) | Apr 27, 2026 2:23:07 PM

## Rule of Thumb for Gain, Aperture, and Beamwidth

*Adapted from a disquisition by Dr. Nathan Cohen, Fractal Antenna Systems, Inc.*

Every antenna has an effective aperture (assuming good efficiency) that can be inferred from the gain.  The effective aperture can then be used to find the full-width-half-maximum (3dB) beamwidth.

### Gain and Diameter

**One can determine the gain of an antenna with this formula:**

$$ G = \frac{4\pi A_e}{\lambda^2} $$

\( A_e \) = effective aperture (m²)  
\( \lambda \) = wavelength (m)

**Effective aperture can be approximated (using an alternative formula for the area of a circle):**

$$ A_e \approx \frac{\pi D^2}{4} $$

**Substituting:**

$$ G = \frac{\pi^2 D^2}{\lambda^2} $$

**Normalized to wavelength:**

$$ G = \pi^2 D_\lambda^2 $$

Where \( D_\lambda = \frac{D}{\lambda} \)

 

**Converting to dBi:**

$$ G_{dBi} = 10 \log_{10}(\pi^2 D_\lambda^2) $$

**Solving for diameter:**

$$ D_\lambda \approx 10^{\frac{G - 10}{20}} $$

 

### Diameter and Beamwidth

The FWHM beamwidth is determined by the effective diameter. The Rayleigh Criterion places it as:

$$ \theta(radians) \approx \frac{1.1 \lambda}{D} $$ 

Normalizing to wavelength and converting to degrees yields:

$$ \theta_{deg} \approx \frac{63}{D_\lambda} $$

### Visualizer (click me)

<https://www.cyntony.com/hubfs/antenna_beams_and_gains_fancy.png>

 

### Summary

These simple relations determine gain, aperture and beamwidth of any antenna system, regardless of wavelength.  

$$ G_{dBi} \approx 10 \log_{10}(\pi^2 D_\lambda^2) $$

$$ D_\lambda \approx 10^{\frac{G - 10}{20}} $$

$$ \theta_{deg} \approx \frac{63}{D_\lambda} $$

Pretty cool, eh?

 

If you'd like to talk about how gain and beamwidth concerns affect your EW or communications system, give us a shout!

[View full post](https://www.cyntony.com/blog/whats-the-beam-for-that-gain)

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