Free-Space Path Loss Calculator

RF path loss is the reduction in signal power as a radio wave travels through free space. Understanding path loss lets ham radio operators calculate the received signal strength, link budgets, and whether a communication path is feasible.

The Free-Space Path Loss (FSPL) Formula:

FSPL (dB) = 20 × log10(d) + 20 × log10(f) + 20 × log10(4π/c)

Simplified to:

FSPL (dB) = 20 × log10(d_km) + 20 × log10(f_MHz) + 32.45

Where:

• d_km = distance in kilometers
• f_MHz = frequency in MHz

Worked Example:

HF communication on 14 MHz (20 meters), distance 500 km (line-of-sight satellite link):

FSPL = 20 × log10(500) + 20 × log10(14) + 32.45 = 20 × 2.699 + 20 × 1.146 + 32.45 = 53.98 + 22.92 + 32.45 = 109.35 dB

VHF repeater on 146 MHz, 50 km:

FSPL = 20 × log10(50) + 20 × log10(146) + 32.45 = 33.98 + 43.29 + 32.45 = 109.72 dB

Link Budget Calculation:

Received power (dBm) = Transmitter power (dBm) + Antenna gains (dBi) − FSPL (dB) − Cable losses (dB)

Example: 100W TX (50 dBm) + 6 dBi Yagi + 6 dBi remote antenna − 109 dB FSPL − 3 dB cable = −50 dBm

Typical VHF receiver sensitivity: −120 dBm → margin of 70 dB — excellent link.

Frequency vs. Path Loss:

Doubling the frequency adds 6 dB of path loss. Doubling the distance adds 6 dB of path loss.

Practical Tips:

• Real-world path loss exceeds FSPL due to terrain, foliage, buildings, and atmospheric effects
• Knife-edge diffraction allows signals to bend over hills with additional diffraction loss (Fresnel zone calculation)
• Use 50Ω systems consistently — impedance mismatches at connectors add unexpected losses