Telecom & Networking
Intermediate

Antenna Gain (dBi)

Directional gain of an antenna relative to an isotropic radiator, in decibels.

Formula

GdBi=10log⁡10GG_{dBi} = 10\log_{10} G

Variables

G_{dBi}Gain (dBi)
GLinear gain ratio

Example

Gain ratio 100: G = 20 dBi

How it works

Antenna gain in dBi tells you how much more strongly an antenna focuses energy in a chosen direction compared with an ideal isotropic radiator, which would spread power equally in all directions. The linear gain ratio is converted to decibels with 10\log_{10} because gain is a power ratio, and the logarithmic scale makes large comparisons easier to handle and add together in link budgets. A higher dBi value means a narrower, more directional radiation pattern, not that the antenna creates extra power.

When to use it

Use this when converting a known linear antenna gain into dBi, or when comparing antennas in RF, Wi‑Fi, cellular, satellite, or radio link design. It is especially useful in link budgets and coverage calculations where gain values are expressed on a logarithmic scale.

Worked example, step by step

Suppose an antenna has a linear gain ratio of G = 15.8. Use the formula: G_dBi = 10 log10(G) Substitute the value: G_dBi = 10 log10(15.8) Calculate the logarithm: log10(15.8) \approx 1.1987 Multiply by 10: G_dBi \approx 10 \times 1.1987 = 11.987 Final answer: G_dBi \approx 12.0 dBi

Common mistakes to avoid

  • Using 20\log10 instead of 10\log10, which is for voltage or field ratios, not power gain
  • Forgetting that dBi is a relative measure compared with an isotropic radiator, not an absolute power unit
  • Applying the formula to a loss value without first converting it to a proper linear gain ratio

Did You Know?

Satellite dishes reach 30-40 dBi by focusing energy into a very narrow beam.

Share this formula

Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026