Antenna Gain Calculator Formula

Understand the math behind the antenna gain calculator. Each variable explained with a worked example.

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Formulas Used

Gain

gain_dbi = 10 * log10(eff_decimal * pow(pi * dish_diameter_m / wavelength_m, 2))

Gain (linear)

gain_linear = eff_decimal * pow(pi * dish_diameter_m / wavelength_m, 2)

Approx Beamwidth

beamwidth_deg = 70 * wavelength_m / dish_diameter_m

Variables

VariableDescriptionDefault
dish_diameter_mDish Diameter(m)1.2
frequency_ghzFrequency(GHz)12
efficiency_pctAperture Efficiency(%)55
wavelength_mDerived value= 0.3 / frequency_ghzcalculated
aperture_areaDerived value= pi * pow(dish_diameter_m / 2, 2)calculated
eff_decimalDerived value= efficiency_pct / 100calculated

How It Works

How Parabolic Antenna Gain is Calculated

Antenna gain measures how effectively the dish concentrates energy compared to an isotropic radiator.

Formula

G = eta x (pi x D / lambda)^2

G(dBi) = 10 x log10(G)

Where D is diameter, lambda is wavelength (c/f), and eta is aperture efficiency (typically 0.5 to 0.7).

The beamwidth approximation is theta = 70 x lambda / D degrees.

Worked Example

A 1.2 m dish at 12 GHz with 55% efficiency.

dish_diameter_m = 1.2frequency_ghz = 12efficiency_pct = 55
  1. 01Wavelength: 0.3 / 12 = 0.025 m
  2. 02pi x D / lambda = 3.1416 x 1.2 / 0.025 = 150.8
  3. 03G linear = 0.55 x 150.8^2 = 0.55 x 22,741 = 12,508
  4. 04G dBi = 10 x log10(12508) = 40.97 dBi
  5. 05Beamwidth: 70 x 0.025 / 1.2 = 1.46 degrees

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