How do you calculate free-space path loss?
Free-space path loss between isotropic antennas is FSPL = (4πd/λ)². In dB with d in km and f in MHz: FSPL = 32.45 + 20·log10(f) + 20·log10(d); with f in GHz and d in m: FSPL = 32.45 + 20·log10(fGHz) + 20·log10(dm). ITU-R P.525 gives the same relationship (32.4 dB constant to one decimal).[1]
What reference values should you know?
| Frequency | 1 m | 100 m | 1 km | 10 km |
|---|---|---|---|---|
| 433 MHz | 25.2 dB | 65.2 dB | 85.2 dB | 105.2 dB |
| 915 MHz | 31.7 | 71.7 | 91.7 | 111.7 |
| 2.45 GHz | 40.2 | 80.2 | 100.2 | 120.2 |
| 5.8 GHz | 47.7 | 87.7 | 107.7 | 127.7 |
| 28 GHz | 61.4 | 101.4 | 121.4 | 141.4 |
Loss rises 6 dB per doubling of distance or frequency.
Is FSPL really a loss?
No energy is absorbed in free space; the “loss” is geometric spreading combined with the shrinking aperture of an isotropic receiving antenna as frequency rises. See Friis equation.
What adds to FSPL in practice?
Atmospheric gases and rain (significant above about 10 GHz; see atmospheric attenuation), diffraction over obstacles, foliage, building penetration, and multipath fading.[2][3]
Frequently asked questions
What is FSPL at 2.4 GHz and 1 km?
About 100 dB.
Does FSPL depend on antenna gain?
No; antenna gains are added separately.
Why 32.45?
It is 20·log10(4π×10⁹/c) for km and MHz units.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Recommendation ITU-R P.525: Calculation of free-space attenuation”. ITU-R. current version.
- “Recommendation ITU-R P.676: Attenuation by atmospheric gases and related effects”. ITU-R. current version.
- “Recommendation ITU-R P.526: Propagation by diffraction”. ITU-R. current version.