# dBi Calculator

dBi stands for deciBel isotropic [1]. It is the gain of an antenna relative to that of a theoretical isotropic antenna [2].

An Isotropic antenna radiates energy equally in all directions. By contrast a Directional antenna focuses energy in a particular direction. The higher the dBi value, the more focused the antenna beam.

Use this Calculator to find the Antenna dBi Gain using:

## dBi Formula

Gain (dBi) = 20*Log10(9.73/[λ*(10)AF/20])

Where

• λ = Wavelength = c/f, where c is the speed of light and f is the frequency
• AF = Antenna Factor

Note that dBi represents a ratio and not an absolute quantity.

Wavelength λ is calculated from frequency

Antenna Factor is specified in dB/m and the equation is:

AF (dB/m) = E (dBV/m) – V (dBV)

where,

• E is the Electric Field
• V is the Voltage induced across the terminals of the antenna

## Example Calculation

If the antenna factor is 30 dB/m for an antenna operating in the 2450 MHz ISM band, the gain is calculated to be 8 dBi.

If the antenna factor is 20 dB/m for an antenna operating in the same band, the gain is calculated to be 18 dBi.

The higher the antenna factor, the poorer the conversion between the E field and voltage induced at the antenna terminals. This results in a lower antenna gain.

### Can the Antenna Gain in dBi be negative?

Yes it can be negative. For instance with a 2.4 GHz antenna, if the antenna factor is 40 dB/m, the antenna gain is -2 dBi. The high antenna factor indicates a high E/V ratio and poor antenna performance.

## Application

The higher the dBi, the more focused the energy and the higher the antenna gain.

Helium hotspot owners use high gain antennas to focus in a direction with larger numbers of witnesses. The highest gain we’ve seen in practical use is 8 dBi.

Many TV antennas are of the directional Yagi-Uda type (shown in the picture below) and can be pointed in the direction of the transmitting tower for better signal reception.

A high gain 26 dBi antenna (shown below) is used for cell phone booster applications. In this case, the antenna is to be pointed in the direction of the nearest cellular base station. An application like Cell Mapper can be used to locate base stations in your vicinity.

## Where is Antenna Gain used?

The range calculator can be used to understand the impact of antenna gain on the range of the communication system. It uses the Free space path loss (FSPL) equations.

The FSPL calculation assumes ideal propagation conditions. For instance, it assumes line-of-sight propagation. But in reality radio propagation at most frequencies should take the curvature of the earth under consideration.

Results from it are therefore very optimistic. However, it can be used to study the relative impact of antenna gain, cable loss, sensitivity and transmit power.

## Related Calculators

Use our

• dBi to dBm converter to calculate the maximum transmit power for a specified EIRP (Effective Isotropic Radiated Power)
• dBm to dBi converter to determine the maximum antenna gain such that the EIRP doesn’t exceed the FCC specified limit.
• V/m to dBm calculator to find the voltage at the input terminal of a radio receiver using the field intensity and the antenna factor. This uses the relationship: V (dBV) = E (dBV/m) – AF (dB/m)

## Notes

Antenna gain is often quoted in manufacturers data sheets. It is inversely proportional to both the Wavelength and the Antenna Factor. In other words, the higher the Wavelength or Antenna factor, the lower the Gain.

## References

[1] DeciBel Antenna Measurements on Wikipedia

[2] Isotropic Radiator on Wikipedia