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:

A 500 km line-of-sight path at 14 MHz (in practice a 500 km 20-meter contact goes by ionospheric skywave, but the free-space figure makes a useful baseline):

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 is around −120 dBm, so that leaves a margin of 70 dB, which is an excellent link.

Enter a transmit power and the two antenna gains above and the calculator runs this whole budget for you, including the margin. Leave them blank and it just gives you the path loss.

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 losses you did not budget for
• Margin is what separates a link that works from one that worked when you tested it. Ten decibels is the usual minimum for anything you intend to rely on