For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
\mathrm{EIRP} = P_t - L_t + G_tdBm
PL(d) = 20\log_{10}\frac{4\pi f}{c} + 10\,n\log_{10}\frac{d}{1\ \mathrm{m}}dB; n = 2 is free space
\mathrm{FSPL} = 32.44 + 20\log_{10} d_\mathrm{km} + 20\log_{10} f_\mathrm{MHz}dB
P_r = \mathrm{EIRP} + G_r - L_r - PL(d) - L_\mathrm{other}dBm
\mathrm{Margin} = P_r - S_\mathrm{rx}dB
d_\mathrm{max} = 10^{\left[\mathrm{EIRP} + G_r - L_r - L_\mathrm{other} - S_\mathrm{rx} - PL(1\ \mathrm{m})\right]/(10n)}m
Variables
| Symbol | Meaning | Unit |
|---|
P_t | Transmitter output power | dBm |
L_t,\ L_r | Cable and connector loss at each end | dB |
G_t,\ G_r | Antenna gain | dBi |
S_\mathrm{rx} | Receiver sensitivity for the data rate or SNR you need | dBm |
n | Path-loss exponent | — |
L_\mathrm{other} | Polarization mismatch, rain, foliage, body loss, etc. | dB |
f,\ d | Frequency, distance | Hz, m |
Typical path-loss exponents
| Environment | n |
|---|
| Free space | 2 |
| Urban area, cellular | 2.7 – 3.5 |
| Shadowed urban | 3 – 5 |
| In building, line of sight | 1.6 – 1.8 |
| In building, obstructed | 4 – 6 |
Worked example
| Input | Value |
|---|
| Frequency | 2.4 GHz |
| Distance | 5 km |
| Tx power | 20 dBm (100 mW) |
| Antenna gains | 12 dBi each |
| Cable loss | 1 dB each end |
| Sensitivity | −90 dBm |
| Path-loss exponent | 2 (free space) |
| Result | Value |
|---|
| EIRP | 31 dBm |
| EIRP | 1.26 W |
| Path loss at 5 km | 114 dB |
| Received power | −72.03 dBm |
| Link margin | 17.97 dB |
| Range at 0 dB margin | 39.57 km |
Common practice is to design for 10 dB or more of fade margin. Weather, vegetation and antenna misalignment all eat into it.
Load this example in the calculator
Validity
- Free space and log-distance only. Terrain, reflections and diffraction are not modeled.
- Free space assumes clear line of sight, with the first Fresnel zone unobstructed.
- Sensitivity depends on data rate and modulation. Take it from the radio’s datasheet for the rate you will run.
Sources
- H. T. Friis, “A Note on a Simple Transmission Formula,” Proc. IRE, vol. 34, no. 5, pp. 254–256, 1946.
- ITU-R Recommendation P.525, Calculation of free-space attenuation.
- T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd ed., Prentice Hall, 2002 (path-loss exponents).