What is the radar range equation?

The radar range equation relates maximum detection range R to transmit power Pt, antenna gain G, wavelength λ, target radar cross section σ, and minimum detectable signal Smin: R^4 = (Pt × G² × λ² × σ) / ((4π)³ × Smin). Taking the fourth root gives maximum range.

What is radar cross section (RCS)?

RCS (σ) is a measure of how detectable an object is by radar. It describes the effective area that intercepts and re-radiates energy back toward the radar. A large aircraft might have an RCS of 10–100 m², while a stealth aircraft can be less than 0.01 m².

Why does range scale as the fourth root of power?

Signal power drops as 1/R² on the outbound path and again as 1/R² on the return path, giving a 1/R⁴ two-way path loss. To double detection range you must increase transmit power by 16×, or improve antenna gain by 4×.

What is system losses and should I include it?

Real radars include system losses (L) from feed losses, atmospheric attenuation, processing losses, etc. The full equation divides the numerator by L. This calculator includes an optional system losses input (default 1, meaning no loss).

What units does this calculator use?

Inputs accept both linear units (watts, m²) and decibel units (dBW, dBm, dBsm). Output range is shown in kilometers, nautical miles, and statute miles.

Radar Range Calculator

Compute maximum radar detection range from transmit power, antenna gain, target RCS, wavelength, and minimum detectable signal.

Radar Parameters

Transmit Power

Antenna Gain

Operating Frequency

Target RCS (Radar Cross Section)

Minimum Detectable Signal (Smin)

System Losses (L)

0 dB = no loss. Typical: 3–10 dB.

Quick Presets

Set parameters and click Calculate

Maximum Detection Range

—

Nautical Miles

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Miles

Derived Parameters

Wavelength (λ) —

Transmit Power (linear) —

Antenna Gain (linear) —

RCS (linear) —

Smin (linear) —

System Losses (linear) —

Radar Range Equation

R = [ (Pt × G² × λ² × σ) / ((4π)³ × Smin × L) ]^1/4

Range Sensitivity (RCS variation)

RCS (m²)	Range (km)	Range (nm)

Summary

The radar range equation determines how far a radar system can detect a target. This calculator takes transmit power, antenna gain, operating frequency, target radar cross section (RCS), system losses, and minimum detectable signal, then solves for maximum range in multiple units. It supports both linear and decibel inputs for engineering convenience.

How it works

Enter the transmitter peak power in watts or dBW.
Input antenna gain and operating frequency (used to derive wavelength).
Enter the target radar cross section (RCS) in square meters or dBsm.
Set the minimum detectable signal (receiver sensitivity) in dBm or watts.
The tool applies the standard radar range equation and displays maximum range in km, nautical miles, and miles.

Use cases

Estimate detection range for ground-based air surveillance radars.
Size radar system parameters during concept design phase.
Verify published radar specifications against the range equation.
Compare performance trade-offs between antenna gain and transmit power.
Determine the effect of target RCS on detection range.
Compute range budget for maritime or weather radar systems.

Frequently Asked Questions

Last updated: 2026-06-14 · Reviewed by Nham Vu