Friis Transmission Equation
The Friis equation gives the power received in a free-space radio link given transmit power, antenna gains, distance, and frequency. It assumes far-field, line-of-sight propagation with no atmospheric loss.
Equations & Parameters ▸
\(P_r = P_t G_t G_r \!\left(\dfrac{\lambda}{4\pi d}\right)^{\!2}\)
| Pₜ | Transmit power (dBm). |
| Gₜ, Gᵣ | Transmit and receive antenna gains (dBi). A half-wave dipole has 2.15 dBi. |
| d | Link distance (m). |
| f | Carrier frequency. Longer wavelengths have less free-space path loss. |
| FSPL | Free-space path loss = 20·log₁₀(4πd/λ) dB. |
| Pᵣ | Received power = Pₜ + Gₜ + Gᵣ − FSPL (in dB arithmetic). |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
dBm
Typical WiFi: 20 dBm = 100 mWdBi
Isotropic = 0, dipole ≈ 2.15dBi
m
Straight-line distanceResults
Path
Free-space path loss (FSPL)—
Received Power
Pᵣ (dBm)—
Pᵣ (watts)—
Diagram