Radar Range Equation Calculator

The radar equation was developed by Sir Robert Watson-Watt\'s team at the UK Air Ministry Research Establishment in 1935 as they designed the Chain Home radar system. The classic monostatic form — R⁴ = (P_t·G²·λ²·σ) / ((4π)³·P_min·L) — has remained unchanged in form since the 1940 MIT Rad Lab\'s formalization.

The fourth-root dependence on power is why radar development focused so heavily on higher antenna gain (G² in the equation, so doubling gain gives 41% more range) rather than more transmitter power (which gives only 19%). WWII-era radar saw antenna diameters grow from 3m (Chain Home) to 10m+ by 1945 — a 4× improvement in area and 16× in effective power-range product.

Modern radars push the equation in different directions: AESA phased-array antennas (electronic beam steering, no mechanical gimbal), ultra-low-noise receivers (cryogenic amplifiers for deep-space), and pulse-compression techniques that trade time-bandwidth for SNR. But the underlying equation is still the one from 1940.

Enter transmitter power (W), monostatic antenna gain (dBi — same antenna for TX and RX), frequency, target radar cross section (σ in m²), receiver minimum detectable signal (dBm), and system losses (dB). The tool solves R⁴ = P_t·G²·λ²·σ / ((4π)³·P_min·L) for the maximum detection range.

For bistatic radars (separate TX and RX antennas), or for integrating N pulses, modify inputs accordingly (2G → G_tx + G_rx; add +10·log(N) to sensitivity for integration gain). For monostatic pulse radars without integration, this is the standard equation. Everything runs client-side.