Calculate maximum radar detection range using the radar range equation. Includes transmit power, antenna gain, RCS, noise figure, and signal-to-noise analysis.
The radar range equation is the fundamental relationship governing how far a radar system can detect a target. It links transmit power, antenna gain, operating frequency, target radar cross section (RCS), and receiver sensitivity into a single maximum detection range. Because range scales with the fourth root of power, intuition is often misleading without doing the math. A large increase in transmitter power may produce only a modest range gain.
This calculator solves the classic radar range equation for both monostatic (co-located Tx/Rx) and bistatic configurations. Enter your system parameters — transmit power, antenna gain, wavelength, RCS, noise figure, bandwidth, and required SNR — and get the maximum detection range along with a complete link budget analysis.
Whether you're an RF engineer designing a new radar, a student studying radar theory, or evaluating surveillance coverage, this tool provides instant parametric analysis with the ability to sweep parameters and compare target types from stealth aircraft to cargo ships.
Use this calculator when you need to estimate detection range from power, gain, wavelength, target size, and receiver sensitivity. It is useful for radar design studies, link-budget checks, and comparing how target RCS changes the result. That makes it easier to see which parameter changes meaningfully move the range and which barely matter.
R_max = ⁴√[(P_t × G² × λ² × σ) / ((4π)³ × k × T × B × F × SNR_min)]. In dB form: 10·log₁₀(R⁴) = P_t(dBW) + 2G(dBi) + 2·10log(λ) + σ(dBsm) − 33·log(4π) − 10log(kTBF) − SNR_min(dB).
Result: 84.5 km maximum detection range
A 1 kW S-band (3 GHz) radar with 30 dBi antenna, 4 dB noise figure, 1 MHz bandwidth, detecting a 1 m² target at 13 dB SNR threshold yields 84.5 km range.
The radar range equation describes the round-trip propagation of electromagnetic energy: out from the transmitter, scattering off the target, and back to the receiver. The (4π)³ factor in the denominator accounts for spherical spreading in both directions plus the scattering process.
Key insight: every parameter is raised to a power of 1 in the R⁴ equation, meaning they all affect R through a 4th root. Doubling any single parameter (power, gain, RCS, wavelength²) only increases range by 2^(1/4) ≈ 19%.
RCS varies enormously: insects ~10⁻⁵ m², birds ~10⁻², small drones ~10⁻², humans ~1 m², cars ~10-100 m², fighter aircraft 1-5 m², stealth aircraft 10⁻³-10⁻¹ m², cargo ships 10³-10⁴ m². RCS also varies with aspect angle — a target's broadside RCS may be 10-20 dB higher than nose-on.
The radar equation is best understood as a power budget in dB: transmit EIRP + target reflection – free-space path loss – receiver noise = received SNR. This linear (in dB) decomposition makes it easy to identify the dominant loss terms and optimize system design. Most design improvements come from antenna gain and receiver sensitivity rather than brute-force transmit power.
Range depends on the 4th root of power — doubling power only increases range by 19% (2^0.25). To double range, you need 16× the power. This is why radar is so power-hungry.
RCS (σ) is the effective area a target presents to the radar, measured in m² or dBsm. A stealth aircraft has ~0.001 m², a fighter ~1-5 m², a cargo ship ~1000+ m².
Typically 10-15 dB for single-pulse detection with Pd ≥ 0.9 and Pfa ≤ 10⁻⁶. Pulse integration can reduce the required single-pulse SNR significantly.
Range ∝ √λ (∝ 1/√f), so lower frequencies achieve longer range for the same power and antenna gain. However, higher frequencies allow smaller antennas for the same gain.
Coherent integration of N pulses improves SNR by N (10·log₁₀(N) dB). Non-coherent integration improves SNR by approximately √N. This is how real radars achieve long range.
Rain, atmospheric gases, and diffraction over Earth's curvature all reduce effective range. This calculator assumes free-space propagation — add 0.5-5 dB for real-world losses.