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 ▸
\(P_r = \dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 R^4}\qquad R_{max}=\left(\dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 P_{min}}\right)^{1/4}\)
| Pₜ | Transmitted power in Watts (W). Enter a linear value, e.g. 10 W = 40 dBm. The calculator uses watts directly. |
| Gₜ, Gᵣ | Transmit and receive antenna gains (dBi). Monostatic radar: Gₜ=Gᵣ. |
| σ | Radar cross-section of the target (m²). Aircraft ≈ 1–100 m², person ≈ 0.1–1 m², bird ≈ 0.01 m². |
| R | Range to target (m). |
| f | Carrier frequency. Sets λ. |
| Pmin | Minimum detectable signal power (dBm). Typically −100 to −120 dBm. |
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
W
dBi
dBi
same as Gₜ for monostaticm²
aircraft≈1–100, person≈0.1–1dBm
receiver sensitivityResults
Performance
Maximum range, R_max—
Received power at 1 km—
Range at Pmin—
Parameters
Wavelength, λ—
EIRP—
Radar equation (dB)—
Diagram