# Free Space Loss Calculator ### Free Space Loss Explanation

The concept of free space loss refers to the natural way radio signal energy gets weaker the further away from the radio signal source you go. Here we describe the mechanisms involved and provide a means to calculate signal energy at a given distance from the source.

There are two main effects which lead to free space loss and non of them are influenced by the frequency of the radiation which is a commonly assumed.

#### First Loss Effect – Radiation Law

Electromagnetic waves propagate energy according to the inverse square law. Which means the energy per unit area away from the transmitting source is inversely proportional to the square of the distance (d) between the source and the observer. So the power per unit area at point d (Pd) away from the source producing power (Ps) is …

#### Second Loss Effect – Antenna Apature

Now the ability of an antenna to absorb this radiated energy depends on its apature which also depends on the wavelength of the radiation. so that the effective power received(Pr) is proportional to the square of wavelength used and the incident power (Pd) at the antenna thus…

#### Equation 2: Pr = Pd x (Wavelength^2/4π)

The free space loss FSP equation is the ratio of transmitted power to received power so…

#### Equation 3:FSP = Ps/Pr

The free space loss FSP = Ps/Pr can be computed by combining Equation 1 with equation 2 and we get…

#### Equation 5:FSPL = (4πdf/c)^2

where…

• f is frequency in herts
• c is speed of light (3 x 10^8 m/s)
• d is distance meters

Note that the appature effect in this equation introduces the frequency (f) element in the equation when we substitute for wavelength. This gives people the impression that free space path loss is dependent on frequency. This is an error as no such mechanism exists in nature.

The loss due to propagation between the transmitting and receiving antennas is called the path loss and can be written in dimensionless form by normalizing the distance to the wavelength:

Loss (dB) = 20×log(4×π×distance/wavelength) (where distance and wavelength are in the same units)

To see how free space loss comes into play when calculating point to point link budgets take a look our page on Link Budget Calculator

Correspondence between free space gain loss in dB and distance in kilometers (km) :

#### Free Space Loss Calculator

Frequency Band:

Loss dB (negative)
kilometers