Formula and Method for Free Space Path Loss
Free space path loss (FSPL) is the reduction in radio signal power that happens simply from a wave spreading out as it travels in a straight, unobstructed line from transmitter to receiver — no reflections, absorption, or obstacles, just geometry. In decibels, FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c), where d is the distance between transmitter and receiver, f is the signal frequency, and c is the speed of light (299,792,458 m/s). This calculator also derives the equivalent linear power ratio and the signal's wavelength, plus an optional estimate of received signal power using the Friis transmission equation.
How the calculation works
Enter the link distance with its unit and the signal frequency with its unit. The calculator converts both to meters and hertz, then computes FSPL(dB) = 20log₁₀(4πdf/c), which expands to the same 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c) form shown above. The wavelength is found from λ = c/f. If you also enter a transmit power and a combined antenna gain (the sum of the transmit and receive antenna gains, in dBi), the tool applies the Friis transmission equation, Pr(dBm) = Pt(dBm) + Gain(dBi) − FSPL(dB), to estimate the power that reaches the receiver.
Common mistakes
- Mixing units: convert distance and frequency to a single consistent pair (for example, meters and hertz) before comparing FSPL across links — this calculator does that conversion for you, but double-check the unit dropdowns match what you intended.
- Treating FSPL as total path loss: FSPL ignores obstacles, multipath, foliage, rain, and atmospheric absorption — real-world loss is almost always higher than the free-space figure, especially indoors or over long terrestrial links.
- Sign errors with antenna gain: in the Friis equation, antenna gain in dBi is added to transmit power, not subtracted — only FSPL itself is subtracted.
Real-world applications
- Wireless link budgeting for Wi-Fi, cellular, satellite, and point-to-point microwave links.
- RF system design — estimating the transmit power or antenna gain needed to close a given communication link.
- Spectrum planning — comparing how different frequency bands affect coverage range for the same power budget.
- Classroom and lab exercises illustrating the inverse-square law and decibel arithmetic in wireless communications.