# Antenna Gain (dBi) to Range Calculator

In this post we provide a tool that calculates the range of a wireless system as a function of the antenna gains.

## Calculator

To calculate the Range, enter the following numbers in the calculator:

• Transmit Antenna Gain (dBi)
• Transmitter Power (dBm)
• Frequency of operation (Hz/kHz/MHz/GHz)
• Total Cable and Other Losses (dB)

## Example Calculation

As an example let’s find the range of an outdoor Wi-Fi network operating at 5 GHz with antenna gain of 2 dBi. The transmit power is +20 dBm and receive sensitivity is -90 dBm. It’s reasonable to expect adapter and connector attenuation of 3 dB.

The range in this case is 1.7 km.

An increase in antenna gain to 10 dBi results in an greater range of 10.7 km.

As the antenna gain increases, the range also increases (when all the other parameters are kept the same).

Note that free space represents the best possible wireless signal coverage.

## Formula

The calculator uses the Free Space Path Loss (FSPL) equation:

FSPL = 20*Log10(d) + 20*Log10(f) + Lc + 20*Log10(4Ï€/c) – GTx – GRx

to calculate d

20*Log10(d) = FSPL – 20*Log10(f) – Lc – 20*Log10(4Ï€/c) + GTx + GRx

d = 10^((1/20)*(FSPL – 20*Log10(f) – Lc – 20*Log10(4Ï€/c) + GTx + GRx))

where the maximum FSPL for the communication system to function is given by the difference between the transmit power and the receive sensitivity.

As an example, if the max transmit power is +20 dBm and the Receiver sensitivity is -90 dBm, then the max FSPL is 110 dB.

## Background

Antenna gain (measured in dBi) is an important parameter that affects the range (or distance) and performance of a communication system. The antenna gain itself is a function of

• Antenna Factor (AF)
• Wavelength (Î»)

Gain (dBi) = 20*Log10(9.73/(Î»*(10)AF/20))

Use this tool to calculate the dBi antenna gain

An antenna with higher gain focuses the energy more effectively in a specific direction, which can result in a longer transmission range because the signal’s power is concentrated rather than spread out in all directions. This is similar to how a flashlight focuses light into a beam to illuminate objects far away.

The picture below shows how increasing antenna gain (from 2 dBi to 9 dBi) results in more focused signal energy in any particular direction, but narrower coverage and longer range.

## Application Examples

### Signal Boosters

Both High gain and low gain antennas are used with signal boosters. As shown in the picture below, the high dBi antenna is outside on the roof. It is pointed in the direction of the cell tower to maximize range.

The inside antenna has lower gain with an omni directional pattern for reception in any room of the house.

Increasing the gain of an antenna can extend its range by focusing the signal more narrowly, which results in less power spread and attenuation over distance. The optimal antenna gain for a specific application depends on the combined set system requirements including range and coverage area.

### Helium / LoRa Antennas

I used an 8 dBi antenna (shown in the picture below) to increase the range on my Helium hotspot. Additionally I moved the antenna to the highest indoor point in the house so that it could emulate free space conditions (although it’s never the case in an urban environment).

The hotspot received more signals when placed here relative to on the ground floor of my house or with a lower gain antenna.