How much a Wi-Fi signal weakens between two antennas in open space, and why. Move the receiver away and watch the inverse square law at work.
At the same distance the power per square metre is the same for every band. What changes is how much of it an antenna can collect: its capture area is λ²/4π, so it shrinks as the wavelength gets shorter. Circles to scale, for a 0 dBi antenna.
Free space path loss (FSPL) is how much weaker a signal is at the receiving antenna than at the transmitting one when nothing but distance is in the way. It has two parts: the energy spreading out over an ever larger sphere (the inverse square law), and the receiving antenna's capture area, which is smaller at higher frequencies. Nothing is used up along the way; the energy is simply spread thinner.
The surface of a sphere grows with the square of its radius, so at twice the distance the same power covers four times the area and each square metre gets a quarter of it. A quarter is −6.02 dB, which is where the rule "double the distance, lose 6 dB" comes from. Ten times the distance gives a hundredth of the power, −20 dB. Try the ×2 button and watch the loss rise by 6.02 dB every time.
Exact: FSPL = 20 log₁₀(4π d f / c), with d in metres, f in hertz and c the speed of light. With d in metres and f in MHz it becomes 20 log₁₀(d) + 20 log₁₀(f) − 27.55. With d in kilometres and f in MHz: 20 log₁₀(d) + 20 log₁₀(f) + 32.44. For example, channel 140 (5700 MHz) at 30 m: 20 log₁₀(0.03) + 20 log₁₀(5700) + 32.44 = 77.1 dB. All three give the same answer to within 0.01 dB.
FSPL is the best case: a clear line of sight with nothing nearby. Indoors, walls, floors, furniture and people absorb and reflect the signal, and reflections arrive by several paths at once, so real signals are usually weaker than this and vary from spot to spot. Use FSPL as the starting point, then allow for everything in the way.
The formula assumes the receiver is well away from the transmitter (the far field). Very close to an antenna it no longer applies, so the distance here starts at 1 m.
The received power is the signal strength the receiver sees, before noise. Whether it's enough depends on the noise and interference around it: the Wi-Fi Modulation Simulator shows why denser modulations need a cleaner signal, and the MCS Index shows the data rates they give.