Explaining Free Space Path Loss
While this is a geometric effect, wavelength is included in the calculation in order to account for the fact that, mathematically, transmission energy is defined as coming from a point source known as an isotropic antenna. An isotropic antenna is defined as an antenna that radiates energy evenly in a perfect sphere with 0 dBi of gain. While defining such an antenna is mathematically convenient, it is physically impossible to build.
The following graph shows the free space path loss for Wi-Fi at 2.4 GHz and 5 GHz.
The following table shows the free space path loss at 1 meter (3 feet) away from the transmitter at various frequencies commonly used in the telecommunications industry.
Per FCC and other worldwide government regulations, a Wi-Fi signal, at most, has a maximum initial power of 30 dBm (1 W, or 1000 mW), and within the first 3 feet over 40 dB of energy is lost (100 W), meaning that the level of exposure 3 feet away is below -10 dBm (0.0001 W, or 0.1 mW).
The propagation of all radio signals is subject to Free Space Path Loss (FSPL), which is a mathematical definition of the geometric property that the further away you are located from the source of a radio transmission, the energy level in that signal drops as a function of the square of the distance. You can think of throwing a pebble into a pond; as the wave ripples out, the energy is spread over a wider and wider area, and the level of energy at any one point is proportionally smaller.
Comparative Example 1: Microwave Oven
A microwave oven operated on the 2.4 GHz bands at around 1000 W (60 dBm). Granted microwaves are shielded, but the shielding is not perfect and deteriorates over time, which is why microwave ovens typically interfere with Wi-Fi when in operation, because they put out more energy on the 2.4 GHz band than an AP and this flood the channel, causing wideband interference. Three feet away from a leaky microwave oven, the 2.4 GHz energy level decreases by 40 dB to 20 dBm (0.1 W, or 100 mW), or about 1000x higher than a Wi-Fi access point.
Comparative Example 2: Ham Radio
A ham radio typically operates at 50 W (47 dBm) at 440 MHz. The FSPL at three feet away (i.e. where the operator is sitting) is about 25 dB (approximately 0.32 W or 320 mW), leading to an exposure level of 22 dBm (0.16 W or 160 mW), or about 1600x higher than a Wi-Fi access point.
Comparative Example 3: Cell Phone
A typical cellular phone operates at 23 dBm (0.25 W or 250 mW). However, it operates very close to your head when on a call (about 2 inches), which provides a minimal FSPL of only 3.5 dB (0.0022 W, or 2.2 mW) at 700 MHz (Verizon LTE). This leads to an exposure level of 19.5 dBm (90 mW or 0.09 W), or approximately 100x higher than a Wi-Fi access point.
You get more exposure to RF energy from using your cell phone, a ham radio, and a microwave oven than you do from a Wi-Fi access point.
Comparative Example 4: Cell Tower
A typical cellular tower operates around 40 W (46 dBm). At 700 MHz (Verizon LTE), the FSPL at about 1/2 mile – 1 mile away is about 90 dB, leading to an exposure level of -44 dBm (0.00004 mW or 0.00000004 W), or about 4000x lower than from a Wi-Fi access point.