RF Toolbox

RF Path Loss Models

Estimates radio propagation loss with the standard models: free-space (line of sight), two-ray ground reflection (with its break-point distance), and the empirical Okumura–Hata / COST-231 models for land-mobile links. Free-space loss is always shown for reference alongside the model you pick.

Equations & Parameters ▸
\(L_{\text{FS}} = 20\log_{10}d_{\text{km}} + 20\log_{10}f_{\text{MHz}} + 32.44\)
\(d_{\text{break}} = \dfrac{4 h_t h_r}{\lambda},\qquad L_{\text{2ray}} = 40\log_{10}d - 20\log_{10}(h_t h_r)\ \ (d > d_{\text{break}})\)
\(L_{\text{Hata}} = 69.55 + 26.16\log_{10}f - 13.82\log_{10}h_b - a(h_m) + (44.9 - 6.55\log_{10}h_b)\log_{10}d\)
fFrequency (MHz). Hata is valid 150–1500 MHz; COST-231 extends it to 1500–2000 MHz.
dPath length (km). Empirical models assume roughly 1–20 km.
ht, hbTransmit / base-station antenna height (m), 30–200 m for Hata.
hr, hmReceive / mobile antenna height (m), 1–10 m. Sets the a(hm) correction.
EnvironmentSelects the model: free-space, two-ray, or urban/suburban/rural (Hata or COST-231, medium-city correction).
References: M. Hata, "Empirical formula for propagation loss in land mobile radio services," IEEE Trans. Veh. Technol., 1980. · COST Action 231, Digital Mobile Radio Towards Future Generation Systems, final report, 1999. · T. S. Rappaport, Wireless Communications, 2nd ed., Prentice Hall, 2002.
Inputs
MHz
Carrier frequency
km
Path length
m
Base height
m
Mobile height
Propagation model
Results

Path loss

Free-space (ref.)
Selected model

Details

Model used
Break-point dist.
Diagram