Radar Range Calculator

Estimate the maximum detection distance of a monostatic radar using the full radar equation. Includes advanced considerations: pulse integration, noise figure, and atmospheric limitations.

1 MW = 1,000,000 W | Peak power for pulsed radar
Typical parabolic: 20-45 dBi; phased array may vary
λ = c / f (c ≈ 299.8 × 10⁶ m/s)
Typical: insect 0.001, person 0.5-1, fighter 1-5, ship >100
Sensitivity at receiver input; can be derived from noise figure
Includes radome, feed, transmission line losses (L>1 reduces range)
Advanced settings (pulse integration, noise figure)
Integration improves SNR by factor np (ideal)
Degrades Smin; 3 dB doubles Smin
For Smin = k T0 B Fn (k=1.38e-23)
These advanced parameters are optional and only affect range if you adjust them. By default they are set to ideal (no integration, noise figure 0 dB).
?️ Long-range surveillance (S band)
✈️ Fighter detection (X band)
⛈️ Weather radar (C band)
? Automotive (77 GHz, RCS=5 m²)
Privacy first: All calculations are performed locally in your browser. No data is sent to any server.

The Radar Range Equation – Full Form

The standard monostatic radar equation relates maximum detection range to system parameters. The basic version used in the calculator is:

Rmax = ⁴√ (Pt G² λ² σ) / ( (4π)³ Smin L ) 

Where:
Pt = transmit power (W), G = antenna gain (linear), λ = wavelength (m), σ = radar cross section (m²),
Smin = minimum detectable signal (W), L = system loss factor (≥1).

Advanced Extensions for Real-World Performance

Pulse Integration

If np pulses are coherently integrated, the SNR improves by a factor np (coherent) or √np (non-coherent). Our calculator applies coherent integration (best case) by dividing Smin by np. Enter np in advanced settings.

Noise Figure & Bandwidth

Smin can be expressed as k T0 B Fn (SNR)min. Here we assume (SNR)min=1 and use the entered Smin directly. Adjusting Fn or B recalculates Smin if desired (see advanced panel).

Key Parameters Explained – With Typical Values

Parameter Symbol Typical Range Impact on Range How to Obtain
Transmit Power Pt W (automotive) … MW (surveillance) R ∝ ⁴√Pt Spec sheet or measurement
Antenna Gain G 10…50 dBi R ∝ √G (since G² under fourth root → √G) From dimensions: G ≈ 4πAe/λ²
Frequency / λ f, λ VHF (100 MHz) … W band (100 GHz) R ∝ √λ (lower frequency gives longer range for fixed gain) Design choice
RCS σ 0.001 m² (insect) … 1000 m² (ship) R ∝ ⁴√σ Estimated from target type or EM simulation
Min. Detectable Signal Smin 10⁻¹⁰ … 10⁻¹⁵ W R ∝ 1/⁴√Smin From receiver noise figure & bandwidth
System Loss L 1…10 R ∝ 1/⁴√L Budgeted from component datasheets
Case Study: AN/FPS-117 Long Range Radar

The AN/FPS-117 is a L-band (1215-1400 MHz) air surveillance radar. Typical parameters: Pt = 2.5 kW (average), G = 28 dBi, σ = 1 m² (fighter), Smin ≈ 5×10⁻¹⁴ W, L = 3. Using the calculator, the theoretical range is ~220 km. In practice, with pulse integration (about 20 pulses) the range extends beyond 250 km, matching its advertised range of 200-250 nm (370-460 km) – note that our simple equation does not include integration gain, elevation coverage, or ducting, which increase effective range.

Step-by-Step Calculation (With Integration Example)

  1. Convert frequency to wavelength: λ = c / f (c = 299,792,458 m/s, f in Hz).
  2. Convert gain from dBi to linear: Glin = 10^(G_dBi / 10).
  3. If pulse integration is used: effective Smin,eff = Smin / np (coherent integration).
  4. If noise figure is entered: Smin can be recalculated as k T0 B 10^(Fn/10). We provide that option separately.
  5. Compute numerator: Pt × Glin² × λ² × σ.
  6. Compute denominator: (4π)³ × Smin,eff × L.
  7. Take the fourth root of (numerator / denominator) to obtain range in meters.
  8. Convert to kilometers if >1000 m.

For very long ranges (above ~300 km), Earth's curvature and atmospheric refraction become dominant. The calculator will display a note when range exceeds 300 km.

Practical Limitations & Mitigations

  • Atmospheric attenuation: At frequencies above 10 GHz, oxygen and water vapor absorb energy. This can be compensated by increasing power or gain.
  • Multipath and interference: Low-elevation targets experience ground reflection, creating lobing. Radar design uses beam shaping to reduce impact.
  • Clutter: Returns from land, sea, or weather can mask targets. MTI and Doppler processing help.
  • Pulse repetition frequency (PRF): Ambiguities in range and Doppler may limit unambiguous range.

Typical Radar Frequency Bands and Characteristics

Band Frequency Typical Use Pros/Cons
HF 3-30 MHz Over-the-horizon radar Very long range, low resolution
VHF/UHF 30-1000 MHz Early warning, wind profilers Good range, large antennas
L-band 1-2 GHz Air traffic control, long range Good all-weather, moderate resolution
S-band 2-4 GHz Surveillance, weather Balance of range & resolution
C-band 4-8 GHz Weather, medium range tracking Higher resolution, more attenuation
X-band 8-12 GHz Fire control, marine radar Good resolution, shorter range
Ku/K/Ka 12-40 GHz Automotive, satellite Very high resolution, heavy attenuation

How to Measure / Estimate Each Parameter

  • Transmit power: From radar specifications or measured at the output.
  • Antenna gain: Calculated from aperture size and efficiency, or measured in an anechoic chamber.
  • Frequency: Design parameter, known.
  • RCS: Complex; often taken from tables (e.g., for aircraft) or computed using electromagnetic software.
  • Smin: Derived from receiver noise figure: Smin = k T0 B Fn (SNR)min. (SNR)min depends on detection probability and false alarm rate.
  • Loss L: Sum of all losses (radome, waveguide, etc.) in linear units.

This tool is developed and maintained by GetZenQuery Tech Team. Algorithms follow standard numerical linear algebra methods and are cross‑validated against authoritative sources (Strang, Lay, MathWorld). Last reviewed: March 2026.

Frequently Asked Questions

Automotive radars typically use low power (10-100 mW) and have wide beamwidths (low gain) for close-range coverage. The high frequency (short λ) also reduces range compared to lower bands. However, they are designed for short ranges (up to 200 m) with high resolution.

Smin = k × T0 × B × 10^(Fn/10) × (SNR)min. Here k = 1.38×10⁻²³ J/K, T0 = 290 K (standard), B is bandwidth (Hz), Fn in dB, and (SNR)min is the required SNR for detection (typically 10-20 dB). Our advanced panel uses this relationship if you provide Fn and B, and we assume (SNR)min = 1 for simplicity.

It comes from the spherical spreading of the wave: the factor 4πR² appears twice (transmit and return paths), and an additional 4π from the effective area of an isotropic antenna. Combined, (4π)³ ≈ 1984.4.

It provides a theoretical maximum under ideal conditions. Real-world factors (atmospheric attenuation, clutter, beam shape, integration, earth curvature) reduce the range. It is an excellent first-order estimator, and with the advanced settings (integration, noise figure) you can get closer to real performance.

dBi is decibels relative to an isotropic radiator. Linear gain = 10^(dBi/10). For example, 30 dBi = 1000 linear gain.

Not directly – the radar equation includes a two-way path. For one-way (e.g., Friis transmission formula), the range dependence becomes 1/R². However, you can adapt it by removing one (4πR²) factor.
References: Radar Tutorial; Skolnik, M. "Introduction to Radar Systems" (3rd ed., 2001); IEEE Std 686™-2017 "IEEE Standard for Radar Definitions"; IEEE Radar Standard.