Free-Space Path Loss (FSPL) Calculator

How it works

FSPL (dB) = 20 log₁₀(d km) + 20 log₁₀(f MHz) + 32.45; P_rx = P_tx + G_tx + G_rx − FSPL − other losses; λ = c ÷ f

Even with nothing in the way, a radio signal weakens with distance because the transmitted energy spreads over an ever-larger sphere; the receive antenna captures a fixed effective area of it, and that area shrinks with the square of frequency. Free-space path loss expresses both effects in decibels: 20 dB per decade of distance and 20 dB per decade of frequency, plus a constant that depends on the units. It is the optimistic floor of any link budget — real paths add diffraction, absorption by walls and foliage, rain fade above 10 GHz and multipath fading — but it explains why 900 MHz LoRa reaches further than 2.4 GHz Wi-Fi with the same power, why satellite links need dishes, and why every 6 dB of extra gain or sensitivity doubles range. Antenna gains are in dBi; if you have dBd, add 2.15.

Worked example

A 5 km, 2.4 GHz link loses 114.0 dB in free space. With 20 dBm transmit power, 15 dBi dishes at both ends and 3 dB of cable and connector loss, the receiver sees −67 dBm — strong enough for a high-rate Wi-Fi bridge; at 10 km it would drop 6 dB to −73 dBm.

Frequently asked questions