What is antenna gain and how is it measured in dBi?

Antenna gain is a measure of how effectively an antenna focuses radiated power in a particular direction relative to a reference antenna. The dBi unit (decibels relative to an isotropic radiator) compares the antenna's peak radiation intensity to a theoretical isotropic antenna that radiates equally in all directions. A gain of 6 dBi means the antenna radiates approximately four times more power in its main direction than an isotropic source would with the same input power. Gain combines two properties: directivity (the geometric focus of the radiation pattern) and radiation efficiency (how much input power is actually radiated rather than lost as heat).

What is the difference between dBi and dBd?

dBi references gain against an isotropic antenna (a mathematical ideal). dBd references gain against a free-space half-wave dipole, which itself has a gain of 2.15 dBi. To convert: dBd = dBi − 2.15. Manufacturers of commercial antennas sometimes quote dBd figures because they appear smaller in magnitude, while datasheets for broadcast and cellular equipment more commonly use dBi. When comparing antennas always confirm which scale is being used — a 5 dBd antenna is actually 7.15 dBi.

How do you calculate the gain of a parabolic or reflector antenna?

Parabolic and reflector antennas are aperture antennas: their gain is determined by their physical size relative to the wavelength. The formula is G = 4π·Ae/λ², where Ae is the effective aperture (Ae = η × A_physical, with η being the aperture efficiency, typically 55–65% for a well-designed parabolic dish). A 1.2-metre dish at 2.4 GHz with 55% efficiency produces approximately 30.3 dBi. Larger dishes and higher frequencies both increase gain, while the wavelength decreases with increasing frequency, making high-frequency aperture antennas especially efficient.

How do you estimate antenna gain from beamwidth?

If you know the radiation pattern but not the physical parameters, gain can be estimated from the half-power beamwidths in the E-plane (θ) and H-plane (φ): G ≈ 41253 / (θ × φ). The constant 41253 represents the total solid angle of a sphere in square degrees. This is an approximation accurate to roughly ±1–2 dB for antennas with a well-defined main lobe and low sidelobe levels. For example, an antenna with 30° × 40° beamwidths gives an estimated gain of about 34.4 linear, or 15.4 dBi. A narrower beamwidth always implies higher gain.

What are typical gain values for dipole, Yagi, patch, and parabolic antennas?

Gain varies enormously by antenna type: a half-wave dipole has 2.15 dBi (the reference for dBd); a quarter-wave monopole over a ground plane achieves about 5.19 dBi; a 3-element Yagi around 8 dBi; a 6-element Yagi approximately 11–12 dBi; a 10-element Yagi up to 14–15 dBi. Patch antennas typically offer 5–9 dBi depending on size and substrate. Small parabolic dishes (0.3 m at 2.4 GHz) reach around 20–22 dBi, while 1.2-metre dishes at the same frequency exceed 30 dBi. Log-periodic antennas fall in the 6–11 dBi range. Higher gain always comes at the cost of a narrower beamwidth.

Science & RF Engineering

Antenna Gain Calculator

Calculate antenna gain in dBi using four standard methods: power ratios, directivity and efficiency, effective aperture (for parabolic dish, reflector, and patch antennas), or half-power beamwidth. Select the method that matches the information you have available.

P_out (radiated power, any unit)

P_in (input power, same unit)

Use any consistent unit (W, mW, µW). Only the ratio P_out / P_in is used — units cancel.

Antenna Gain (dBi)

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Gain (dBd, relative to dipole)—

Gain (linear power ratio)—

What is antenna gain?

Antenna gain describes how effectively an antenna concentrates radiated power in the direction of maximum radiation, compared to a reference antenna fed with the same input power. It is not amplification — antennas are passive devices. Gain is produced by focusing: an antenna that radiates strongly in one direction necessarily radiates less in others. The result is that a high-gain antenna can deliver significantly more power to a receiver in its main beam than a low-gain antenna would, without any change in transmitter power.

Gain is almost always expressed in decibels. The dBi scale references the isotropic antenna — a theoretical point source that radiates equally in all directions (a perfect sphere). The dBd scale references the free-space half-wave dipole, which has a gain of 2.15 dBi. Converting between them: dBd = dBi − 2.15. Always check which scale a manufacturer is using before comparing antenna specifications.

Gain is the product of two underlying properties: directivity (how sharply the radiation pattern is focused, a purely geometric property) and radiation efficiency (the fraction of input power that is actually radiated rather than dissipated as heat in the conductor or dielectric). A highly directive antenna with significant ohmic losses may have lower gain than a moderately directive but very efficient one.

Which formula to use and when

1. From power ratios

Use this when you have measured or simulated power values — for example, from a network analyser or a radiation pattern measurement in an anechoic chamber. P_out is the radiated power in the direction of maximum radiation; P_in is the accepted input power. Units must be consistent but otherwise do not matter.

G (dBi) = 10 × log₁₀( P_out / P_in )

2. From directivity and efficiency

Use this when antenna simulation software (such as NEC, HFSS, or CST) gives you the directivity and you separately know or estimate the radiation efficiency. This method separates the geometric and loss contributions to gain and is useful when optimising antenna designs.

G = η × D η = radiation efficiency (0 to 1) D = directivity (linear or convert from dBi: D = 10^(D_dBi / 10))

3. From effective aperture — parabolic dish, reflector, and patch antennas

Use this for any aperture-type antenna where the physical collecting area is known. The effective aperture Ae accounts for the aperture efficiency η (typically 55–65% for a well-illuminated parabolic dish, 70–90% for a large horn antenna). Wavelength λ = c / f where c = 299,792,458 m/s. This is the standard formula for satellite dishes, reflector arrays, and large patch arrays.

G = (4π × Ae) / λ² Ae = η × A_physical (effective aperture, m²) λ = c / f (wavelength in metres) c = 299,792,458 m/s f in Hz For a circular dish of diameter d: A_physical = π × (d / 2)²

4. From half-power beamwidth

Use this quick estimate when only the radiation pattern is available — common when evaluating measured antenna patterns or when working from a datasheet that quotes beamwidth but not gain. θ is the E-plane HPBW (the angle between the −3 dB points in the elevation cut) and φ is the H-plane HPBW (in the azimuth cut), both in degrees. The approximation assumes a well-shaped main beam with low sidelobe levels and is accurate to ±1–2 dB for most directive antennas.

G ≈ 41253 / (θ_HPBW × φ_HPBW) θ = E-plane half-power beamwidth (degrees) φ = H-plane half-power beamwidth (degrees) 41253 = total solid angle of a sphere in square degrees (= 360² / π)

Typical gain values by antenna type

Understanding where your calculated value sits relative to common antenna types helps validate results and informs system design decisions such as link budget, beamwidth trade-offs, and mounting requirements.

Isotropic antenna — 0 dBi. The mathematical reference. Does not physically exist but defines the dBi scale.

Half-wave dipole — 2.15 dBi (0 dBd). The practical reference for the dBd scale. Omnidirectional in the azimuth plane. Standard reference for FM broadcast and many VHF/UHF systems.

Quarter-wave monopole over a ground plane — approximately 5.19 dBi. Used extensively in mobile, automotive, and base station antennas where a ground plane is present.

Patch antenna (single element) — 5–9 dBi. Gain depends on substrate permittivity, thickness, and patch dimensions. A single-element patch at 2.4 GHz typically achieves 6–8 dBi. Patch arrays can reach 15–20 dBi or more.

3-element Yagi — approximately 7–8 dBi. Common in UHF television reception and 70 cm amateur radio. Compact and efficient for moderate gain requirements.

6-element Yagi — approximately 10–12 dBi. Used in point-to-point Wi-Fi links, APRS, and digital TV fringe reception.

10-element Yagi — approximately 14–15 dBi. Long-boom design used in 2 m and 70 cm DX amateur radio communications, weather satellite reception, and fixed wireless.

Log-periodic dipole array (LPDA) — 6–11 dBi. Broadband by design; gain is moderate and relatively constant across a wide frequency range. Used in EMC testing and broadband monitoring.

Small parabolic dish (0.3 m, 2.4 GHz) — approximately 20–22 dBi. Entry-level point-to-point Wi-Fi links and radio astronomy demonstrations.

Medium parabolic dish (1.2 m, 2.4 GHz) — approximately 30–32 dBi. Long-range point-to-point links; requires careful alignment due to a beamwidth of only 2–3°.

Large satellite dish (3 m, Ku-band 12 GHz) — approximately 48–50 dBi. Direct broadcast satellite reception, VSAT terminals, deep-space communication ground stations.

Common questions

Antenna gain is a measure of how effectively an antenna focuses radiated power in a particular direction relative to a reference antenna. The dBi unit (decibels relative to an isotropic radiator) compares the antenna's peak radiation intensity to a theoretical isotropic antenna that radiates equally in all directions. A gain of 6 dBi means the antenna radiates approximately four times more power in its main direction than an isotropic source would with the same input power. Gain combines two properties: directivity (the geometric focus of the radiation pattern) and radiation efficiency (how much input power is actually radiated rather than lost as heat).
dBi references gain against an isotropic antenna (a mathematical ideal). dBd references gain against a free-space half-wave dipole, which itself has a gain of 2.15 dBi. To convert: dBd = dBi − 2.15. Manufacturers of commercial antennas sometimes quote dBd figures because they appear smaller in magnitude, while datasheets for broadcast and cellular equipment more commonly use dBi. When comparing antennas always confirm which scale is being used — a 5 dBd antenna is actually 7.15 dBi.
Parabolic and reflector antennas are aperture antennas: their gain is determined by their physical size relative to the wavelength. The formula is G = 4π·Ae/λ², where Ae is the effective aperture (Ae = η × A_physical, with η being the aperture efficiency, typically 55–65% for a well-designed parabolic dish). A 1.2-metre dish at 2.4 GHz with 55% efficiency produces approximately 30.3 dBi. Larger dishes and higher frequencies both increase gain, while the wavelength decreases with increasing frequency, making high-frequency aperture antennas especially efficient.
If you know the radiation pattern but not the physical parameters, gain can be estimated from the half-power beamwidths in the E-plane (θ) and H-plane (φ): G ≈ 41253 / (θ × φ). The constant 41253 represents the total solid angle of a sphere in square degrees. This is an approximation accurate to roughly ±1–2 dB for antennas with a well-defined main lobe and low sidelobe levels. For example, an antenna with 30° × 40° beamwidths gives an estimated gain of about 34.4 linear, or 15.4 dBi. A narrower beamwidth always implies higher gain.
Gain varies enormously by antenna type: a half-wave dipole has 2.15 dBi (the reference for dBd); a quarter-wave monopole over a ground plane achieves about 5.19 dBi; a 3-element Yagi around 8 dBi; a 6-element Yagi approximately 11–12 dBi; a 10-element Yagi up to 14–15 dBi. Patch antennas typically offer 5–9 dBi depending on size and substrate. Small parabolic dishes (0.3 m at 2.4 GHz) reach around 20–22 dBi, while 1.2-metre dishes at the same frequency exceed 30 dBi. Log-periodic antennas fall in the 6–11 dBi range. Higher gain always comes at the cost of a narrower beamwidth.