Radar Range Equation

Formula

Description

The radar range equation determines the maximum detection range of a radar system. The transmitted power spreads over a sphere (1/R²), reflects off the target (with radar cross section σ), spreads again on the return path (another 1/R²), and must exceed the receiver minimum detectable signal. The fourth-root dependence means that doubling the range requires 16× the transmit power. This equation is fundamental to radar system design for military, weather, aviation, automotive, and maritime applications.

Variables

• P_t — Transmitter peak power (W)
• G_t — Transmit antenna gain (linear, not dB)
• G_r — Receive antenna gain (linear, not dB)
• λ — Wavelength (m)
• σ — Target radar cross section (m²)
• S_min — Minimum detectable signal power (W)

Practical Notes

Typical radar cross sections: bird 0.01 m², person 1 m², car 10-200 m², aircraft 1-100 m², ship 1000-100000 m². Antenna gains must be in linear (not dB): G_linear = 10^(G_dB/10). The equation assumes free-space propagation; atmospheric attenuation, multipath, and clutter reduce actual range. To convert S_min from dBm: S_min_W = 10^((dBm-30)/10).