The free space path calculator provides the attenuation or loss of a signal as it propagates through free space.

To calculate the **FSPL**, enter the following:

- Frequency of operation
**f** - Distance
**d** - Transmit Antenna Gain
**G**_{Tx} - Receive Antenna Gain
**G**_{Rx}

## Formula

**FSPL = 20*Log _{10}(d) + 20*Log_{10}(f) + L_{c} + 20*Log_{10}(4π/c) – G_{Tx} – G_{Rx}**

★ This formula only applies when the distance (**d**) between the antennas is large enough that the antennas are in the **far field **of each other. In other words **d >> λ** where λ = c/f. **It is sufficient if the distance is at least 10 times larger than the wavelength.**

**Definition of Terms**

Below is a list of the terms used in the calculator and what each of them mean.

**Frequency of operation**

This is the frequency at which the communication system operates.

**Transmit Antenna Gain**

This depends on the type of antenna used and is expressed in **dBi **(dB relative to isotropic antenna).

**Receive Antenna Gain**

Depends on antenna used and is expressed in dBi. In cases where the signal is from a particular direction, a high gain antenna (8 dBi for instance) can be used. This allows focusing of energy instead of receiving from all directions. It can be calculated from the Antenna Factor and frequency of operation.

*The free space path loss equations assume an ideal operating environment i.e. an unobstructed propagation path between transmitter and receiver*.

**Example Calculation**

At a frequency of 100 kHz and a distance of 100 km, the attenuation or **FSPL = 52.45 dB**.

At a frequency of 100 kHz and distance of 100 meters, the **FSPL = -7.55 dB** which is clearly an erroneous result as the attenuation cannot be negative.

To understand this, let’s take into consideration the requirement that for the equation to be valid the distance **d** has to be at least **10*λ** = **2998 meters** (using the frequency to wavelength calculator). The calculator is therefore applicable at distances greater than 29980 meters or 30 km.