Free-space path loss (FSPL) calculator
Free-space path loss is the signal loss between two isotropic antennas with nothing in the way — no absorption, just the wave spreading over an ever-larger sphere. It is the floor under every link budget: FSPL(dB) = 32.45 + 20·log₁₀(d in km) + 20·log₁₀(f in MHz), so ten times the distance or ten times the frequency each cost 20 dB.
The green curve is free-space loss against distance at your frequency; the grey curves are fixed references at 900 MHz and 5.8 GHz, and the dot marks the distance you entered. The distance axis is logarithmic, so every decade adds 20 dB and the curves come out straight.
Assumes isotropic antennas, far field and truly empty space. Any real path adds loss on top.
How it works
- 01
Understand what “loss” means here
Free space absorbs nothing. The transmitted power spreads over the surface of an expanding sphere, so a fixed-size receiving antenna intercepts an ever-smaller share of it. Power density falls as 1/d2, which is why doubling the distance costs 6 dB and never less.
- 02
Apply the formula
In practical units, FSPL (dB) = 32.45 + 20·log10(d in km) + 20·log10(f in MHz). Distance and frequency both enter through a 20·log10 term, so each factor of ten adds 20 dB. At 2.4 GHz that means 80 dB over 100 m, 100 dB over 1 km and 120 dB over 10 km.
- 03
Read the frequency term correctly
Empty space does not attenuate high frequencies more. The frequency term comes from the reference antenna: an isotropic antenna captures energy over an effective aperture of λ2/4π, which shrinks as the wavelength shrinks. Keep the physical antenna size fixed — a dish, for example — and its gain rises with frequency, cancelling the term and often beating it.
- 04
Add the real-world losses on top
FSPL is the best case and nothing more. Terrain diffraction, buildings, foliage, rain above roughly 10 GHz and multipath fading all add to it, frequently by tens of dB. Supplying those terms is the job of a link budget and of a terrain-aware coverage simulation.
Formulas
- FSPL — free-space path loss, dB
- d — path length, km
- f — frequency, MHz
- 32.45 — the constant that ties km and MHz together (32.4478 exactly)
- d — path length, m
- f — frequency, Hz
- c — speed of light in vacuum, 299 792 458 m/s
Worked example
- d = 10 km, f = 2400 MHz
- 20·log10(10) = 20.0 dB
- 20·log10(2400) = 67.6 dB
- FSPL = 32.45 + 20.0 + 67.6 = 120.05 dB
- → the signal arrives about 1012 times weaker, and that is the best case
FAQ
- Why does path loss increase with frequency if free space absorbs nothing?
- Because the formula is referenced to isotropic antennas, and an isotropic antenna collects power over an area of λ2/4π. At 5.8 GHz that area is about 42 times smaller than at 900 MHz, which is exactly the 16.2 dB difference the formula shows over the same distance. Give both links the same physical antennas and the difference disappears.
- How much does doubling the distance cost?
- Exactly 6.02 dB, at any frequency, because the distance term is 20·log10(d). Ten times the distance adds 20 dB and a hundred times adds 40 dB. A 1 km hop at 2.4 GHz sees about 100 dB of free-space loss; the same link stretched to 10 km sees 120 dB.
- Is FSPL the loss I will actually see?
- No — it is the floor. Real paths add terrain diffraction, wall and foliage penetration, rain attenuation and fading, which together commonly run 10 to 40 dB above the free-space value and much more in dense urban or wooded terrain. Use FSPL as a sanity check, then budget the rest on top.
- Does FSPL apply indoors?
- Only as a lower bound over the first few metres. Indoor propagation is dominated by walls, floors and multipath: a plasterboard wall costs a few dB, a reinforced concrete floor 10–20 dB or more. Indoor models such as ITU-R P.1238 replace the 20·log10(d) term with a steeper distance exponent and a floor-penetration term.
FSPL is the physics floor. Waveshed computes what terrain adds on top — line-of-sight and signal coverage over real elevation data, free in your browser.
Simulate the real path →Related guides
- LOS vs RF (FSPL & ITM) — when a clear sight line answers the question and when path loss decides
- Plan radio coverage (RF / ITM) — the workflow that turns these numbers into a coverage map over real terrain
Sources & further reading
- ITU-R Recommendation P.525 — Calculation of free-space attenuation ↗ — the standard defining this calculation
- H. T. Friis, “A Note on a Simple Transmission Formula”, Proc. IRE, 1946 ↗ — the original paper, via DOI
- Free-space path loss — Wikipedia ↗ — derivation, variants and worked numbers