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
Radar Equation helps you calculate design values for a radar engineering project from 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). Calculate received power, link margin, signal delay, effective aperture, and key radar metrics for a monostatic target in free space including system losses. Use the result to make an informed first design decision before choosing hardware, setting dimensions, or evaluating the RF system in its final environment.
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
This radar engineering calculation is based on 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). Real-world accuracy depends on factors such as material properties, losses, mounting, nearby conductors, ground interaction, feed-line effects, and construction tolerance. Confirm the final system with measurement or simulation.
Build and Tuning Notes
Apply the radar equation result as an initial target, then validate it in the intended installation. Keep the physical layout and feed arrangement consistent while testing, change one parameter at a time, and record the measured outcome before making another adjustment.
Frequently Asked Questions
What does the Radar Equation calculate?
Calculate received power, link margin, signal delay, effective aperture, and key radar metrics for a monostatic target in free space including system losses. The calculation provides an initial design value based on 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).
Which inputs are needed for the Radar Equation?
Enter 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) using the displayed units. Each value directly affects the calculated result, so confirm the unit and operating conditions before running the calculation.
How accurate is this radar equation?
It follows 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). It is accurate for the formula assumptions, but installed performance can change because of materials, loss, environment, mounting, nearby objects, and measurement uncertainty.
What should I do after using the Radar Equation?
Compare the result with the practical constraints of your radar engineering system, then validate the completed design with appropriate measurement equipment or simulation.
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.