Radar Equation Calculator
Calculate received power, link margin, signal delay, effective aperture, and key radar metrics for a monostatic target in free space including system losses.
8
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
P_r = (P_t · G_t · G_r · λ² · σ) / ((4π)³ · R⁴ · L) | λ = c/f | G = 10^(G_dBi/10) | L = 10^(L_dB/10)This formula is used to calculate antenna parameters for radar equation calculator.
Overview
The Radar Equation Calculator computes received echo power ($P_r$), link margin, signal propagation delay, effective antenna aperture ($A_e$), and two-way free-space path loss for monostatic radar systems operating in free space.
Input Guide
Enter Peak Transmit Power (P_t), Transmit Antenna Gain (G_t), Receive Antenna Gain (G_r) [Equal to G_t for Monostatic], Operating Frequency (f), Target Radar Cross Section (σ), Target Range (R), Total System Losses (L) [Atmosphere, Feed, Cable, Processing], Receiver Sensitivity / Minimum Detectable Signal (MDS) exactly in the units shown by this radar equation. 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.
- Transmit Antenna Gain (G_t) — use dBi.
- Receive Antenna Gain (G_r) [Equal to G_t for Monostatic] — use dBi.
- Operating Frequency (f) — use GHz.
- Target Radar Cross Section (σ) — use m².
- Target Range (R) — use km.
- Total System Losses (L) [Atmosphere, Feed, Cable, Processing] — use dB.
- Receiver Sensitivity / Minimum Detectable Signal (MDS) — use dBm.
Output Guide
The results describe the calculated radar equation 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 Equation uses P_r = (P_t · G_t · G_r · λ² · σ) / ((4π)³ · R⁴ · L) | λ = c/f | G = 10^(G_dBi/10) | L = 10^(L_dB/10). Supply Peak Transmit Power (P_t) (W), Transmit Antenna Gain (G_t) (dBi), Receive Antenna Gain (G_r) [Equal to G_t for Monostatic] (dBi), Operating Frequency (f) (GHz), Target Radar Cross Section (σ) (m²), Target Range (R) (km), Total System Losses (L) [Atmosphere, Feed, Cable, Processing] (dB), Receiver Sensitivity / Minimum Detectable Signal (MDS) (dBm) in the displayed units, then use the calculated values as the first engineering target for this radar engineering design or analysis.
Design Notes
The classical monostatic radar equation follows the inverse fourth-power law ($P_r \propto \frac{1}{R^4}$), meaning doubling the target distance reduces received power sixteenfold ($12 \text{ dB}$ attenuation). System link budget analyses must account for peak transmitted power ($P_t$), transmit/receive antenna gains ($G_t, G_r$), operating wavelength ($\lambda$), target Radar Cross Section ($\sigma$), and total system loss factors ($L$). Minimum detectable signal (MDS) threshold determines maximum operational detection range.
Build and Tuning Notes
Total system loss ($L$) encompasses RF transmission feed losses, radome absorption, atmospheric/precipitation attenuation, beam-shape loss, polarization mismatch, and signal processing losses. To maintain detection margins above receiver sensitivity, optimize antenna effective aperture ($A_e = \frac{G \lambda^2}{4\pi}$) or integrate multiple pulse returns via coherent or non-coherent integration.
Frequently Asked Questions
What is the standard monostatic radar equation formula?
The standard monostatic radar equation with losses is $P_r = \frac{P_t \cdot G_t \cdot G_r \cdot \lambda^2 \cdot \sigma}{(4\pi)^3 \cdot R^4 \cdot L}$. It relates transmitted power to received echo power over a round-trip path.
Why does received power drop off with the fourth power of range (1/R⁴)?
Radar power experiences spherical spreading twice: first from the transmit antenna out to the target ($1/R^2$), and second as the target scatters the reflected echo energy back to the radar receiver ($1/R^2$). Multiplying these geometric spreading factors yields the overall $1/R^4$ relationship.
What constitutes total system loss (L) in radar link budgets?
System losses include RF feed line/waveguide insertion loss, radome attenuation, atmospheric gaseous absorption, rain attenuation, beam-shape/scanning losses, Doppler filter straddling loss, and processing losses in receiver circuitry.
How is detection margin calculated against receiver sensitivity?
Detection margin (link margin) is calculated as $\text{Margin (dB)} = P_r \text{ (dBm)} - \text{MDS (dBm)}$, where MDS is the Minimum Detectable Signal (receiver sensitivity threshold). A positive margin indicates the target echo is detectable above noise.
How do you calculate round-trip signal propagation time?
Because radar signals travel at the speed of light ($c \approx 3 \times 10^8 \text{ m/s}$) to the target and back, round-trip delay is $t = \frac{2R}{c}$. For example, a target at $10 \text{ km}$ yields a round-trip signal delay of approximately $66.7 \text{ } \mu\text{s}$.
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.