Free-Space Path Loss Calculator — Friis Equation
Free-Space Path Loss (FSPL) quantifies how much signal power a radio wave loses as it travels through free space. Enter the line-of-sight distance and signal frequency to get the path loss in decibels — the key input for any wireless link budget.
km
GHz
Signal power lost over the line-of-sight path — before antenna gain or other losses
- 1
20·log₁₀(distance)
20 × log₁₀(10) = 20Distance in km; every doubling adds 6 dB. - 2
20·log₁₀(frequency)
20 × log₁₀(2.4) = 7.6042Frequency in GHz; every doubling adds 6 dB. - 3
Free-Space Path Loss
20 + 7.6042 + 92.4478 = 120.05The constant 92.44 dB comes from 20·log₁₀(4π × 10¹² / c).
How does this calculator work?
FSPL (dB) = 20·log₁₀(d km) + 20·log₁₀(f GHz) + 92.44. Every doubling of distance adds 6 dB; every doubling of frequency adds 6 dB. FSPL is the geometric lower-bound loss used as the baseline for wireless link budgets — add atmospheric absorption, rain margin and obstacle losses for a complete real-world budget.
Formula
How this is calculated
When a radio wave travels through free space, its power spreads over an ever-larger spherical wavefront. Even without any physical obstacle, absorption, or multipath, the received power decreases with the square of distance — a consequence of geometry, not material losses. The Friis transmission equation describes the received power as Pr = Pt + Gt + Gr − FSPL (in dBm/dB), where Pt is the transmitter power, Gt and Gr are antenna gains, and FSPL is the free-space path loss.
FSPL (linear) = (4πdf/c)², where d is distance in metres, f is frequency in hertz, and c is the speed of light (≈ 299,792,458 m/s). Expressed in dB, this becomes FSPL = 20·log₁₀(4πdf/c). Substituting d in kilometres and f in gigahertz simplifies the constant to 92.44 dB, giving the convenient two-variable formula above. Notice that doubling the distance adds 6 dB; doubling the frequency also adds 6 dB.
FSPL is an idealised lower bound — real wireless links add attenuation from atmospheric gases, rain, obstacles (building penetration loss), and multipath fading, which engineers budget separately as margins on top of FSPL. Use FSPL as the starting point for a link budget and add those margins to determine the required transmit power, antenna gain or maximum range for a given receiver sensitivity.
Frequently asked questions
Physically, a higher-frequency signal has a shorter wavelength, which means a fixed-aperture antenna captures a smaller fraction of the incoming power (effective aperture ∝ λ²). FSPL models this with the 20·log₁₀(f) term — every doubling of frequency adds 6 dB of path loss.
Yes — FSPL is the foundation of link budgets for any radio system. Wi-Fi at 2.4 GHz over 100 m gives about 80 dB FSPL; 5G mmWave at 28 GHz over 100 m gives about 101 dB. Geostationary satellite links at 14 GHz over 36,000 km exceed 205 dB FSPL, driving the need for large dish antennas and high-power amplifiers.
Path loss (including FSPL) is a single loss term. A link budget is a complete accounting of all gains and losses: transmit power + transmit antenna gain − FSPL − cable/connector losses − atmospheric losses + receive antenna gain = received power. The margin above the receiver sensitivity threshold determines link reliability.
Also known as
TG we-Calculate Editorial Team. (2026). Free-Space Path Loss Calculator — Friis Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/free-space-path-loss-calculator
TG we-Calculate Editorial Team. "Free-Space Path Loss Calculator — Friis Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/free-space-path-loss-calculator.
TG we-Calculate Editorial Team, "Free-Space Path Loss Calculator — Friis Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/free-space-path-loss-calculator
@misc{wecalculate_free_space_path_loss_calculator, title = {Free-Space Path Loss Calculator — Friis Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/free-space-path-loss-calculator}}, year = {2026}, note = {TG we-Calculate} }
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