Monostatic Radar Range Equation & Received Echo Power (dBm) Calculator

Evaluate two-way 1/R⁴ radar echo power (dBm) and maximum detection range.

Received Radar Echo Power (P_r)
-88.96 dBm
Round-Trip Pulse Echo Delay 100.07 μs
Radar Carrier Wavelength (λ) 3.19 cm
Echo Power at 2× Range (−12.04 dB) -101 dBm
Inputs
⚡ Scenarios:
W
Radar peak transmit power P_t in Watts.
dBi
Monostatic radar antenna gain G in dBi.
GHz
Radar operating frequency in GHz (e.g., 9.4 GHz X-band, 77 GHz automotive).
m²
Target Radar Cross Section σ in m² (e.g., 1 m² small craft, 10 m² aircraft/ship).
km
Target slant range R in kilometers.
Results & Graph
Received Radar Echo Power (P_r)
-88.96 dBm
Round-Trip Pulse Echo Delay
100.07 μs
Radar Carrier Wavelength (λ)
3.19 cm
Echo Power at 2× Range (−12.04 dB)
-101 dBm

Received Radar Echo Power (P_r)

Graph 1 • Radar Range Equation • Domain Architecture & Live Telemetry Maps Transmit Peak Power Watts, Antenna Gain Dbi, Radar Frequency Ghz through Radar Range Equation Formula.
Source / Tx Target / Rx Radar Range Equation Propagation Path Received Radar Echo Power -88.96 dBm Round-Trip Pulse Echo Dela: 100.07 μs Radar Carrier Wavelength (: 3.19 cm
Graph 2 • Received Radar Echo Power (P_r) Across Transmit Peak Power Watts Sweep (40% → 160%) Evaluates P_r = (P_t × G² × λ² × σ) / [ (4π)³ × R⁴ ] across 7 operating points (current input highlighted).
-92.94 dBm -45.92 dBm 1.10 dBm -92.94 2.0kW -91.17 3.0kW -89.93 4.0kW -88.96 5.0kW -88.16 6.0kW -87.50 7.0kW -86.92 8.0kW
Graph 3 • Joint Sensitivity: Transmit Peak Power Watts × Antenna Gain Dbi Compares Received Radar Echo Power (P_r) when Antenna Gain Dbi is shifted +25% (solid) vs. −25% (dashed).
-106.5 dBm -52.71 dBm 1.10 dBm --- Antenna Gain Dbi @ 75% -74.51 -30% -73.66 -15% -72.96 +0% -72.35 +15% -71.82 +30%
Summary: At 15 km on a 10 m² RCS target (9.4 GHz, 32 dBi gain), received echo power is -88.96 dBm and round-trip pulse time-of-flight is 100.07 μs.
Summary: At 15 km on a 10 m² RCS target (9.4 GHz, 32 dBi gain), received echo power is -88.96 dBm and round-trip pulse time-of-flight is 100.07 μs.
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Formula & Mathematical Methodology: Radar Range Equation Formula

Pr = (Pt × G² × λ² × σ) / [ (4π)³ × R⁴ ]
P_r = (P_t × G² × λ² × σ) / [ (4π)³ × R⁴ ]
  • transmitPeakPowerWatts: Transmit Peak Power Watts (W)
  • antennaGainDbi: Antenna Gain Dbi (dBi)
  • radarFrequencyGhz: Radar Frequency Ghz (GHz)
  • targetRcsSqMeters: Target Rcs Sq Meters (m²)
  • targetRangeKm: Target Range Km (km)

Rounding: Engineering outputs round to 2–3 decimal places; discrete material bag/unit counts round up via ceiling.

Worked Example: Engineering Scenario: Radar Range Equation

Evaluate two-way 1/R⁴ radar echo power (dBm) and maximum detection range.

  1. Enter your system dimensions, electrical/RF ratings, or environmental conditions.
  2. Evaluate the governing equation: P_r = (P_t × G² × λ² × σ) / [ (4π)³ × R⁴ ].
  3. Inspect the primary design output, supporting allowances, and 3 SVG schematics.
Result: Computes Radar Range Equation via P_r = (P_t × G² × λ² × σ) / [ (4π)³ × R⁴ ].

Frequently Asked Questions

How does the Monostatic Radar Range Equation & Received Echo Power (dBm) Calculator calculate results?

It evaluates P_r = (P_t × G² × λ² × σ) / [ (4π)³ × R⁴ ] directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for a required dimension or rating?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input parameter.

Does this engineering calculator work offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Science & Engineering · RF, Telecom & Antenna Engineering

Monostatic Radar Range Equation & Received Echo Power (dBm) Calculator: inputs, method, and how to read the result

Evaluate two-way 1/R⁴ radar echo power (dBm) and maximum detection range.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Transmit Peak Power Watts: Radar peak transmit power P_t in Watts.
  • Antenna Gain Dbi: Monostatic radar antenna gain G in dBi.
  • Radar Frequency Ghz: Radar operating frequency in GHz (e.g., 9.4 GHz X-band, 77 GHz automotive).
  • Target Rcs Sq Meters: Target Radar Cross Section σ in m² (e.g., 1 m² small craft, 10 m² aircraft/ship).

What the calculation includes

With the default values shown, Received Radar Echo Power (P_r) is -88.96 dBm. The calculation follows Radar Range Equation Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Transmit Peak Power Watts from 5,000 W to 5,500 W changes Received Radar Echo Power (P_r) from -88.96 dBm to -88.54 dBm. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard NREL, IEEE, ASHRAE, and IRC design equations.
  • Verify final structural, electrical, and mechanical specifications against local building codes.

Scope: Global Engineering & Building Code Standard Check the assumptions and limitations against your situation before relying on the estimate.

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