Radar Tool

Radar range equation

Estimate maximum detection range from transmit power, antenna gain, frequency, target radar cross-section, receiver threshold and losses.

Radar range equation

R_max = ⁴√P_t · G² · λ² · σ(4π)³ · P_min · L

Received echo power decreases with the fourth power of range. Solving for range therefore requires the fourth root.

Parameters:

P_t is transmit power. G is antenna gain and appears squared because the same antenna transmits and receives. λ is wavelength. σ is target radar cross-section in square metres. P_min is the minimum detectable received power. L represents system and propagation losses.

With all other parameters unchanged, doubling detection range requires sixteen times the transmit power.

Inputs

Transmit power P_t (kW) Peak pulse power. Airport surveillance radars are typically tens of kW to low MW.

Antenna gain G (dBi) A large rotating dish is typically 30–40 dBi.

Frequency (GHz) S-band ≈ 3 GHz, X-band ≈ 10 GHz.

Target radar cross-section σ

Minimum detectable signal P_min (dBm) Set by receiver noise. −110 dBm is a reasonable classroom value.

System losses L (dB) Cables, radome, atmosphere, processing. 4–8 dB is typical.

Result

Maximum detection range—

Wavelength λ—

Echo power at that range—

Echo power at half that range—

The cyan curve shows received echo power against range, decreasing by approximately 12 dB each time range doubles. Its crossing with the amber P_min line marks the modelled detection limit.

This model assumes single-pulse detection and excludes integration gain, clutter and target fluctuation statistics.