Radar Range Equation Calculator
Solve the radar equation for maximum detection range, received power, or required transmit power. Includes RCS, system losses, and integration gain.
How to Use
- Enter TX power, antenna gain, frequency, target RCS, RX sensitivity, and system losses.
- Result: maximum detection range under given SNR requirement.
Show Work
Formulas
History of the Radar Equation
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.
About This Calculator
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.
About the Radar Range Equation Calculator
Radar Range Equation Calculator is a quick, free tool for electronics and circuit design. It works in your browser and keeps everything on your device. Solve the radar equation for maximum detection range, received power, or required transmit power. Includes RCS, system losses, and integration gain.
How it works
Enter your figures and the result appears instantly, updating the moment you change anything. There is no submit button and nothing to wait for, so it is easy to try a few what-if numbers and compare the results. Just check each box holds the kind of value it expects.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What is RCS?
Radar Cross Section: the effective area of a target as seen by radar. A sphere of area A has RCS = A; a flat-plate reflector is much larger; stealth aircraft minimize RCS to < 0.01 m².
Why fourth root?
Signal travels out (r²) and back (r²), so round-trip energy falls as 1/r⁴. Doubling TX power only adds 19% range (2^(1/4) = 1.19).
What is integration gain?
Summing multiple pulses improves SNR. N coherent pulses: +10log(N) dB gain. 100 pulses = 20 dB effective sensitivity improvement.
How do I use the Radar Range Equation Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Airport Radar
10 MW peak at S-band, 40 dB antenna, 1 m² target RCS: ~200 km range.
Automotive Radar
1 W at 77 GHz, 25 dB gain, 10 m² RCS: ~250 m range.
Weather Radar
Nexrad WSR-88D: 750 kW, 45 dBi, 0.01 m² RCS (raindrop): ~200 km.
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