Antenna Gain Conversion
Gain conversion
Enter a gain (dBi or dBd); the conversion, linear gain, and optional EIRP appear live.
Gain
How to use this calculator
Antenna gain can be referenced to an isotropic radiator (dBi) or to a half-wave dipole (dBd). A dipole has a gain of ≈ 2.14 dBi, so dBd = dBi − 2.14 and dBi = dBd + 2.14. Enter a gain in either unit and the calculator converts it, shows the linear gain, and — if you enter a transmitter power — computes the EIRP (Effective Isotropic Radiated Power) and the far-field electric field strength at 1 m.
What it means in a real circuit
An antenna rated 10 dBd is 10 + 2.14 = 12.14 dBi. If you feed it with 1 W, the EIRP is 1 W × 10^(12.14/10) ≈ 16.4 W (12.14 dBW). The field strength at 1 m in free space is √(30 × EIRP) ≈ 22.2 V/m. Use this to compare antennas rated in different units, to estimate how much power is actually radiated, and to predict received signal strength over a link.
Definitions
dBi: gain relative to an isotropic radiator (a theoretical point source that radiates equally in all directions). dBd: gain relative to a half-wave dipole. 2.14 dBi: the gain of a half-wave dipole, which is the reference for dBd. Linear gain: 10^(dB/10), a ratio of power. EIRP: the power that would have to be fed to an isotropic antenna to produce the same peak field as your actual antenna.
Design tips
Always note whether a spec is dBi or dBd — a 10 dBd antenna is actually 12.14 dBi. When comparing antennas, convert to the same reference. For link budgets, EIRP (in dBW or dBm) is the standard quantity. Remember that gain is directional — a high-gain antenna radiates more in one direction and less in others.
Common mistakes
Confusing dBi and dBd (a 2.14 dB error). Forgetting that gain is a ratio, not an absolute — "10 dBi" means 10× the power of an isotropic source in that direction. Assuming gain is the same in all directions (it isn't — it's a 3D pattern). Using EIRP for a directional antenna without accounting for the pattern.
Component-selection / practical advice
For a link budget, convert everything to dBm or dBW and add: EIRP(dBm) = P(dBm) + G(dBi) − feeder loss. A 1 W (30 dBm) transmitter with a 12 dBi antenna and 2 dB of loss gives 40 dBm EIRP. Use this to predict received power and check it's above your receiver's sensitivity.
Limitations
The 2.14 dBi figure is for an ideal half-wave dipole in free space; real dipoles can vary slightly. The field-strength calculation assumes free space and the far field; near-field, ground reflection, and impedance mismatches change the real value. Gain is a 3D pattern — the calculator shows the peak (main beam) gain, not the gain in other directions.
Example use cases
Comparing a 7 dBi patch antenna to a 10 dBd Yagi; computing the EIRP for a point-to-point link budget; predicting received signal strength over a known path; converting a manufacturer's spec to a common reference.
Frequently asked questions
dBi is referenced to an isotropic radiator; dBd is referenced to a half-wave dipole. Since a dipole is 2.14 dBi, dBd = dBi − 2.14. A 10 dBd antenna is 12.14 dBi.
dBd = dBi − 2.14, and dBi = dBd + 2.14. The calculator does this automatically based on the unit you select.
Effective Isotropic Radiated Power — the power that would have to be fed to an isotropic antenna to produce the same peak field. EIRP(dBW) = P(W) + 10·log10(P) + G(dBi), or in dB: EIRP(dBm) = P(dBm) + G(dBi) − loss.
A half-wave dipole is a real antenna that radiates more in some directions than an isotropic source. Its directivity works out to ≈ 2.14 dBi, which is the reference for the dBd unit.
Mixing up dBi and dBd (a 2.14 dB error), assuming gain is the same in all directions, or forgetting feeder loss in a link budget.