🚀 Radar Range Equation Calculator

The radar range equation links the performance of a radar to its hardware and the target. In its common form the maximum range is R₀ = [ (Pₕ·G²·λ²·σ) / ( (4π)³·k·T·B·F·SNRₖ) ) ]^1/4, where Pₕ is peak transmit power, G is antenna gain, λ wavelength, σ the target's radar cross-section (RCS), and the denominator collects the noise terms: Boltzmann's constant k, system temperature T, bandwidth B, noise figure F, and the required signal-to-noise ratio SNR.

The fourth-root behavior is the most important practical fact in radar: to double the detection range you need 16 times the transmit power, all other things equal. It is also why radar designers obsess over receiver noise — improving the noise figure by 1 dB extends range by about 6% without spending a watt more.

The calculator takes the system parameters in SI units, computes the wavelength from frequency, and applies the radar equation with a default system temperature of 290 K and a bandwidth you specify. The result is the theoretical maximum range for a single pulse at the required SNR. Additional factors — losses, pulse integration, atmospheric attenuation — can be folded into the SNR or noted separately.

The derived minimum detectable signal for the given SNR is a useful companion number — it tells you the power threshold the receiver must resolve. For a full picture of how the target appears to a communications link rather than a radar, see the Friis path loss calculator.

1. Enter peak transmit power in watts.
2. Enter frequency in MHz or GHz.
3. Enter antenna gain in dBi (use the same value for TX and RX).
4. Enter target RCS in m² (see the reference table).
5. Set receiver noise figure, bandwidth and required SNR.
6. Click Calculate to get the max range in km, miles and nautical miles.

Why is the range proportional to the fourth root of power?

The wave spreads once on the way to the target and again on the way back, so the echo follows a 1/R⁴ law instead of the 1/R² of a one-way link. Taking the fourth root of the whole equation means range changes slowly with power — doubling range needs 16× power.

What RCS should I use for a typical aircraft?

A light aircraft presents roughly 1–10 m² depending on aspect (side-on is larger, nose-on smaller). Modern fighters with stealth shaping drop to fractions of a square metre. For initial estimates, 2–5 m² is a reasonable civil-aircraft figure.

How does pulse integration help?

Coherently integrating N pulses improves the effective SNR by up to 10·log₁₀(N) dB. Integrating 100 pulses adds up to 20 dB of effective sensitivity, which dramatically extends range without higher peak power — the standard trick of modern radars.

Does the noise figure really matter that much?

Yes. The noise figure sits in the denominator under a fourth root, so every 1 dB saved in the receiver equals about 6% more range, or equivalently allows a smaller, cheaper transmit chain for the same range.

What is the effect of weather on the equation?

The equation assumes free space. Rain and fog add one-way attenuation that grows with frequency above 10 GHz. At X-band (10 GHz) heavy rain can add 1–10 dB of one-way loss over long paths, which is a major factor in weather radar design.

Can I use this for an automotive radar?

As a starting point, yes. Automotive radars at 77 GHz use the same equation with short ranges (100–300 m), tiny antennas, and heavy pulse/chirp processing. The 77 GHz wavelength is short, which keeps the antennas small but makes rain attenuation and beamwidth management critical.

Because range scales as the fourth root, improve the receiver first: every dB of noise-figure improvement buys about 6% more range, the same gain as every dB of transmit power. Pulse integration (N pulses) improves SNR by up to 10·log₁₀(N) dB, which is why coherent radars integrate many pulses. The RCS of a real target fluctuates wildly with aspect angle — the table values are ballpark averages, not guarantees. Attenuation in rain matters above 10 GHz and must be subtracted from the single-pulse budget. Remember the radar horizon: even a perfect radar cannot see beyond the radio horizon, so check the line-of-sight calculator for ground-based systems.