Path Loss

The idea

Imagine spraying water from a hose: up close the spray is strong and concentrated; far away it spreads thin. Radio waves spread the same way — outward in an ever-growing sphere, with the same total energy stretched over a bigger and bigger surface. Path loss is how much weaker a signal gets while traveling, even through perfectly empty space with no obstacles at all.

Because the sphere's area grows with distance squared, doubling the distance makes the signal 4 times weaker, not 2 times. At 1 m from your router you have full strength; at 2 m, 25 percent; at 10 m, just 1 percent. This is the inverse square law, and in dB language it becomes a pair of rules worth memorizing:

• Double the distance → +6 dB more loss
• Double the frequency → +6 dB more loss (each ×10 of either adds 20 dB)

Some reference numbers: 2.4 GHz WiFi at 100 m loses about 80 dB; 5 GHz WiFi at the same distance about 86 dB (higher frequency, more loss); a 900 MHz cell signal at 1 km about 91 dB; a GPS satellite 20,000 km away about 182 dB. An 80 dB loss means the received power is 100 million times weaker than transmitted — and receivers decode it routinely.

Real signals also punch through stuff, and each obstacle takes a toll. From worst blocker to best: metal (nearly a total wall — filing cabinets, elevators, mirror backings), water (fish tanks, wet walls, and people — we are about 60 percent water), concrete and brick (the classic "dead bedroom" cause), wood and drywall (a few dB each), and glass and plastic (almost transparent).

The math

Free space path loss (FSPL) in decibels:

$$FSPL_{dB} = 20\log_{10}(d) + 20\log_{10}(f) + 20\log_{10}\left(\frac{4\pi}{c}\right)$$

where d is distance in meters, f is frequency in Hz, and c is the speed of light. Both 20·log terms grow by 6 dB per doubling — that is where the doubling rules come from. The frequency term does not mean space is "thicker" at high frequencies; a smaller wavelength means a matched receiving antenna is physically smaller and catches a smaller slice of the passing wave.

Quick check: 2.4 GHz at 50 m gives about 74 dB; move to 100 m and it becomes about 80 dB — exactly +6.

Common misconceptions

• Myth: Doubling the distance halves the signal. Reality: It quarters it (−6 dB). Energy spreads over an area that grows with distance squared.
• Myth: Path loss means the air absorbs the signal. Reality: Free-space loss is pure geometric spreading — it happens even in a vacuum. Absorption by rain, walls, and people is an extra cost on top.
• Myth: 5 GHz WiFi is weaker because it travels slower. Reality: All radio waves travel at the speed of light. 5 GHz has roughly 6 dB more path loss than 2.4 GHz plus worse wall penetration — speed has nothing to do with it.

Try it

Open the Path Loss Calculator, enter 2.4 GHz at 50 m, then double the distance and the frequency in turn — watch each doubling add exactly 6 dB. The RF Propagation lab shows the same fading visually with obstacles in the way.