Antenna Beamwidth
θ = 70 × λ / D
Quick answer
This calculator solves θ ≈ 70 × λ / D for Beamwidth. With Wavelength 1 m, Aperture Diameter 2.2 m, the result is 31.82 °. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The half-power (-3 dB) beamwidth of a circular aperture antenna is approximately 70 times the wavelength divided by the aperture diameter, measured in degrees. This relationship applies to dish antennas, horn antennas, and phased arrays. Larger apertures and shorter wavelengths produce narrower beams with higher gain. The constant 70 is an approximation that varies between 58-75 depending on the illumination taper of the aperture. Narrower beamwidth means higher gain but requires more precise pointing.
Variables
- θ — Half-power beamwidth (degrees)
- λ — Wavelength (m)
- D — Antenna aperture diameter (m)
Practical Notes
A 1-meter dish at 10 GHz (λ=0.03m) has a beamwidth of about 2.1°, requiring precise pointing for satellite or microwave links. Antenna gain is inversely proportional to beam solid angle: G ≈ 27000/(θ_az × θ_el) for a pencil beam. Amateur radio EME (moonbounce) stations typically use dishes or large Yagi arrays with beamwidths of 5-15° at UHF/microwave frequencies.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| theta | Beamwidth | ° | ° |
| lambda | Wavelength | m | mm, cm, m, km |
| D | Aperture Diameter | m | mm, cm, m, km |
Step by step
- 1. What you know: Wavelength 1 m, Aperture Diameter 2.2 m
- 2. The relation: θ ≈ 70 × λ / D
- 3. Substitute: lambda = 1 m, D = 2.2 m
- 4. Result: Beamwidth = 31.82 °
Worked examples
Minimum range
Given: Wavelength 1 mm, Aperture Diameter 2.2 mm
Result: Beamwidth = 31.82 °
Low range
Given: Wavelength 10 mm, Aperture Diameter 2.2 cm
Result: Beamwidth = 31.82 °
Typical
Given: Wavelength 1 m, Aperture Diameter 2.2 m
Result: Beamwidth = 31.82 °
High range
Given: Wavelength 100 m, Aperture Diameter 0.22 km
Result: Beamwidth = 31.82 °
Maximum range
Given: Wavelength 1 km, Aperture Diameter 2.2 km
Result: Beamwidth = 31.82 °
Solving for each variable
Solve for Beamwidth
Wavelength 1 mm, Aperture Diameter 2.2 mm → 31.82 °
Solve for Wavelength
Beamwidth 1.5 °, Aperture Diameter 2.2 mm → 0.04714 mm
Solve for Aperture Diameter
Beamwidth 1.5 °, Wavelength 1 mm → 4.667 cm
How Beamwidth changes with Wavelength
| Wavelength (input) | Beamwidth (result) |
|---|---|
| 10 cm | 3.182 ° |
| 25 cm | 7.955 ° |
| 50 cm | 15.91 ° |
| 0.75 m | 23.86 ° |
| 1 m | 31.82 ° |
| 1.5 m | 47.73 ° |
| 2 m | 63.64 ° |
| 4 m | 127.3 ° |
| 7 m | 222.7 ° |
| 10 m | 318.2 ° |
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<p><a href="https://vbatpower.com/formulas/antenna-beamwidth/">Antenna Beamwidth</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Antenna Beamwidth?
Use θ ≈ 70 × λ / D. With Wavelength 1 m, Aperture Diameter 2.2 m, Beamwidth works out to 31.82 °.
What is the formula for Antenna Beamwidth?
The formula is θ ≈ 70 × λ / D. The half-power (-3 dB) beamwidth of a circular aperture antenna is approximately 70 times the wavelength divided by the aperture diameter, measured in degrees.
How do you find Wavelength when you know the other values?
Rearrange for Wavelength: with Beamwidth 1.5 °, Aperture Diameter 2.2 mm, Wavelength is 0.04714 mm.
How do you find Aperture Diameter when you know the other values?
Rearrange for Aperture Diameter: with Beamwidth 1.5 °, Wavelength 1 mm, Aperture Diameter is 4.667 cm.
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