How do you calculate free-space path loss?
Free-space path loss (FSPL) is the loss between two isotropic antennas in free space: FSPL = (4πd/λ)², or in decibels FSPL = 32.45 + 20·log10d(km) + 20·log10f(MHz), as standardized in ITU-R P.525.[1] It rises 6 dB per doubling of distance or frequency.
What are typical FSPL values?
| Frequency | 10 m | 100 m | 1 km | 10 km |
|---|---|---|---|---|
| 433 MHz | 45.2 dB | 65.2 dB | 85.2 dB | 105.2 dB |
| 915 MHz | 51.7 dB | 71.7 dB | 91.7 dB | 111.7 dB |
| 2.45 GHz | 60.2 dB | 80.2 dB | 100.2 dB | 120.2 dB |
| 5.8 GHz | 67.7 dB | 87.7 dB | 107.7 dB | 127.7 dB |
| 28 GHz | 81.4 dB | 101.4 dB | 121.4 dB | 141.4 dB |
Why does FSPL depend on frequency?
The dependence comes from the isotropic receiving antenna’s effective aperture λ²/4π, not from any loss in space. With fixed-size apertures at both ends, received power increases with frequency.[2] See effective aperture.
When is FSPL not enough?
Near the ground, through buildings and over long paths, additional mechanisms apply: ground reflection (two-ray model), diffraction over obstacles (ITU-R P.526), atmospheric absorption and rain (atmospheric attenuation), and indoor losses (ITU-R P.1238).[3][4]
Frequently asked questions
What is the 32.45 constant?
20·log10(4π/c) with d in km and f in MHz; with d in m and f in MHz it becomes −27.55.
Is FSPL different for directional antennas?
FSPL is defined between isotropic antennas; antenna gains are added separately.
Does air absorb signals?
Very little below about 10 GHz, except in specific absorption bands at higher frequencies.
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 edition.
- “A Note on a Simple Transmission Formula”. H. T. Friis, Proceedings of the IRE, vol. 34, no. 5, pp. 254-256. May 1946.
- “Recommendation ITU-R P.526: Propagation by diffraction”. ITU-R. current edition.
- “Recommendation ITU-R P.1238: Propagation data and prediction methods for the planning of indoor radiocommunication systems”. ITU-R. current edition.