RF Toolbox

Radar Range Equation Calculator

The radar equation relates transmitted power, antenna gains, target radar cross-section, and range to determine the received signal power. Use it to calculate maximum detection range, minimum detectable RCS, or required transmit power.

Equations & Parameters ▸
\(P_r = \dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 R^4}\qquad R_{max}=\left(\dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 P_{min}}\right)^{1/4}\)
PₜTransmitted power in Watts (W). Enter a linear value, e.g. 10 W = 40 dBm. The calculator uses watts directly.
Gₜ, GᵣTransmit and receive antenna gains (dBi). Monostatic radar: Gₜ=Gᵣ.
σRadar cross-section of the target (m²). Aircraft ≈ 1–100 m², person ≈ 0.1–1 m², bird ≈ 0.01 m².
RRange to target (m).
fCarrier frequency. Sets λ.
PminMinimum detectable signal power (dBm). Typically −100 to −120 dBm.
Physical constants used
cSpeed of light = 2.998×10⁸ m/s
µ₀Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m
ε₀Permittivity of free space = 8.854×10⁻¹² F/m
Inputs
W
dBi
dBi
same as Gₜ for monostatic
aircraft≈1–100, person≈0.1–1
dBm
receiver sensitivity
Results

Performance

Maximum range, R_max
Received power at 1 km
Range at Pmin

Parameters

Wavelength, λ
EIRP
Radar equation (dB)
Diagram