Antenna Gain
G = 10 × log₁₀(4πAe/λ²)
Quick answer
This calculator solves G = 10 × log₁₀(4πAe/λ²) for G. With Effective Aperture 100 cm², Wavelength 1 m, the result is -9.008 dBi.
Calculator
Formula
Description
Antenna gain relates the effective aperture area of an antenna to the wavelength of the signal. A larger effective area captures more of the incoming wavefront, producing higher gain. The gain is referenced to an isotropic radiator (dBi), which is a theoretical point source radiating equally in all directions. This formula shows that for a fixed physical size, gain increases with frequency (shorter wavelength). This is why dish antennas and horn antennas become increasingly effective at higher frequencies. The effective area is typically smaller than the physical area due to aperture efficiency (typically 50-70% for parabolic dishes).
Variables
- G — Antenna gain (dBi)
- Ae — Effective aperture area (m²)
- λ — Wavelength (m)
Practical Notes
Typical antenna gains: dipole 2.15 dBi, patch antenna 6-9 dBi, Yagi 6-15 dBi, parabolic dish 20-40+ dBi. Higher gain antennas have narrower beamwidths: a 20 dBi dish has a beamwidth of about 10-15 degrees. For omnidirectional coverage, use low-gain antennas; for point-to-point links, use high-gain directional antennas.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Ae | Effective Aperture | m² | mm², cm², m² |
| lambda | Wavelength | m | mm, cm, m, km |
Step by step
- 1. What you know: Effective Aperture 100 cm², Wavelength 1 m
- 2. The relation: G = 10 × log₁₀(4πAe/λ²)
- 3. Substitute: Ae = 100 cm², lambda = 1 m
- 4. Result: G = -9.008 dBi
Worked examples
Minimum range
Given: Effective Aperture 10 mm², Wavelength 1 mm
Result: G = 20.99 dBi
Low range
Given: Effective Aperture 1 cm², Wavelength 10 mm
Result: G = 10.99 dBi
Typical
Given: Effective Aperture 100 cm², Wavelength 1 m
Result: G = -9.008 dBi
High range
Given: Effective Aperture 1 m², Wavelength 100 m
Result: G = -29.01 dBi
Maximum range
Given: Effective Aperture 10 m², Wavelength 1 km
Result: G = -39.01 dBi
How G changes with Effective Aperture
| Effective Aperture (input) | G (result) |
|---|---|
| 10 cm² | -19.01 dBi |
| 25 cm² | -15.03 dBi |
| 50 cm² | -12.02 dBi |
| 75 cm² | -10.26 dBi |
| 100 cm² | -9.008 dBi |
| 150 cm² | -7.247 dBi |
| 200 cm² | -5.998 dBi |
| 400 cm² | -2.987 dBi |
| 0.07 m² | -0.5569 dBi |
| 0.1 m² | 0.9921 dBi |
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<p><a href="https://vbatpower.com/formulas/antenna-gain/">Antenna Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Antenna Gain?
Use G = 10 × log₁₀(4πAe/λ²). With Effective Aperture 100 cm², Wavelength 1 m, G works out to -9.008 dBi.
What is the formula for Antenna Gain?
The formula is G = 10 × log₁₀(4πAe/λ²). Antenna gain relates the effective aperture area of an antenna to the wavelength of the signal.
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