Radar Range Calculator
Estimate maximum monostatic radar detection range in free space including system losses and flexible sensitivity units.
6
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
R_max = [ (P_t · G² · λ² · σ) / ((4π)³ · S_min · L) ]^(1/4)This formula is used to calculate antenna parameters for radar range calculator.
Overview
The Radar Range Calculator estimates the maximum theoretical detection range ($R_{\text{max}}$) for monostatic radar systems operating in free space, accounting for transmit power, antenna directivity, target radar cross-section (RCS), receiver sensitivity, wavelength, and total system insertion losses.
Input Guide
Enter Peak Transmit Power (P_t), Antenna Gain (G), Operating Frequency (f), Target RCS (σ), Min Detectable Signal (S_min), Total System Losses (L) exactly in the units shown by this radar range. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Peak Transmit Power (P_t) — use W.
- Antenna Gain (G) — use dBi.
- Operating Frequency (f) — use GHz.
- Target RCS (σ) — use m².
- Min Detectable Signal (S_min) — use dBm.
- Total System Losses (L) — use dB.
Output Guide
The results describe the calculated radar range values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.
How This Calculator Works
The Radar Range uses R_max = [ (P_t · G² · λ² · σ) / ((4π)³ · S_min · L) ]^(1/4). Supply Peak Transmit Power (P_t) (W), Antenna Gain (G) (dBi), Operating Frequency (f) (GHz), Target RCS (σ) (m²), Min Detectable Signal (S_min) (dBm), Total System Losses (L) (dB) in the displayed units, then use the calculated values as the first engineering target for this radar engineering design or analysis.
Design Notes
The fundamental radar equation exhibits a fourth-root range dependence ($R_{\text{max}} \propto \sqrt[4]{P_t}$), requiring a 16-fold ($12 \text{ dB}$) increase in transmitted power or target RCS to double the maximum operational range. Operating frequency ($f$) directly determines wavelength ($\lambda = \frac{c}{f}$), impacting effective antenna aperture size and propagation characteristics. Sensitivity threshold ($S_{\text{min}}$ or MDS) is derived from receiver noise floor ($k T_0 B F$) and the required signal-to-noise ratio (SNR) for a given probability of detection and false alarm rate.
Build and Tuning Notes
System loss ($L$) accounts for transmission line RF attenuation, radome losses, atmospheric absorption, beam-shape/scanning losses, and signal processing degradation. Convert all gain and loss factors from decibels ($10^{\text{dB}/10}$) and convert minimum detectable signal from $\text{dBm}$ to linear Watts ($10^{(S_{\text{min}}-30)/10}$) when calculating maximum distance. The maximum un-ambiguous range is also bounded by the Pulse Repetition Frequency (PRF), where $R_{\text{unambiguous}} = \frac{c}{2 \cdot \text{PRF}}$.
Frequently Asked Questions
What is the maximum radar range equation formula?
The monostatic radar range equation is $R_{\text{max}} = \left[ \frac{P_t \cdot G^2 \cdot \lambda^2 \cdot \sigma}{(4\pi)^3 \cdot S_{\text{min}} \cdot L} \right]^{1/4}$, where $P_t$ is peak transmit power, $G$ is directive antenna gain, $\lambda$ is wavelength, $\sigma$ is radar cross-section, $S_{\text{min}}$ is minimum detectable signal, and $L$ represents total system losses.
Why does doubling radar range require 16 times more transmitter power?
Radar energy experiences spherical path loss twice: outbound from transmitter to target ($1/R^2$) and inbound from target back to receiver ($1/R^2$). Combining these results in a total $1/R^4$ power drop-off, which yields a fourth-root relationship ($R \propto \sqrt[4]{P_t}$) when solving for maximum detection range.
How is receiver sensitivity (S_min) determined?
Minimum detectable signal ($S_{\text{min}}$) is calculated using $S_{\text{min}} = k \cdot T_0 \cdot B \cdot F \cdot (S/N)_{\text{min}}$, where $k$ is Boltzmann’s constant, $T_0$ is system noise temperature ($290 \text{ K}$), $B$ is noise bandwidth, $F$ is receiver noise figure, and $(S/N)_{\text{min}}$ is the required signal-to-noise ratio for detection.
How do you convert maximum range to round-trip delay time?
Electromagnetic waves travel at light speed ($c \approx 2.998 \times 10^8 \text{ m/s}$). The round-trip time delay is $t = \frac{2 R_{\text{max}}}{c}$. For example, a target at $100 \text{ km}$ produces an echo return delay of approximately $667.1 \text{ } \mu\text{s}$.
What factors are included in total system loss (L)?
Total system loss ($L$) aggregates transmitter feed losses, receiver line losses, radome transmission loss, beam-shape/scanning factor, integration loss, atmospheric gas absorption, and Doppler processing losses.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.