Radar Range Equation Calculator
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Peak power for pulsed radars, average for CW/FMCW. Marine 4–25 kW; ATC 1–5 MW peak; automotive 10 mW–1 W.
IEEE 521 bands: L 1–2; S 2–4; C 4–8; X 8–12; Ku 12–18; Ka 27–40; W 75–110 GHz.
Gain over isotropic. Marine 25–32 dBi; ATC 33–40 dBi; high-gain dish 45–50 dBi.
Insect −50 dBsm; bird −20 dBsm; person 0 dBsm; fighter +5 dBsm; airliner +20 dBsm; cargo ship +40 dBsm.
Mode selection, range targets, pulse width and bandwidth, noise figure and temperature, system and atmospheric losses, configuration, pulse integration, antenna heights (all optional — defaults handle typical screening).
Overview
The Radar Range Equation Calculator computes the maximum detection range, signal-to-noise ratio, EIRP, minimum detectable signal, and range regime for monostatic or bistatic pulsed radar systems. It covers three engineering workflows in one tool: maximum range at a chosen SNR threshold, SNR at a fixed target range, and design verification against a required range with deficit analysis.
The calculator handles IEEE 521 radar bands from L through W, pulse integration (coherent and non-coherent), iterative atmospheric loss correction, radio horizon estimation from antenna heights, and bistatic configurations with separate transmit and receive gains and ranges. Outputs appear in both linear and decibel form for every quantity engineers reason about in dB.
Status classification uses a two-track architecture. Track A reports the primary compliance status: NORMAL (green), EXTREME-RANGE (amber, sanity flag above 5,000 km), INSUFFICIENT-RANGE (amber, design target missed), or INFEASIBLE (gray, invalid inputs). Track B classifies the operational regime: SHORT-RANGE, MEDIUM-RANGE, LONG-RANGE, or VERY-LONG-RANGE. When Track A is NORMAL, the combined badge reads "NORMAL / MEDIUM-RANGE" (or whichever Track B applies).
The calculator targets first-order system-level engineering trade studies and education. It does not model clutter, Doppler processing, pulse compression, detection statistics (Pd, Pfa), or FMCW chirp processing. For those workflows, dedicated tools are required.
How to Use This Calculator
Enter Transmitted Power (P_t) — peak power for pulsed radars, average for CW/FMCW. Select unit: W, kW, MW, dBW, or dBm.
Enter Operating Frequency (f) — carrier frequency in MHz or GHz. The calculator derives wavelength λ = c / f.
Enter Antenna Gain (G) — gain over isotropic in dBi or as a linear ratio.
Enter Target RCS (σ) — radar cross-section in m² or dBsm.
Click Calculate — maximum detection range, SNR, EIRP, MDS, noise power, and range regime appear.
Expand Show advanced parameters to enter SNR threshold, pulse width, noise figure, system losses, bistatic configuration, pulse integration, or antenna heights for radio horizon.
Use design verification mode — fill Required Range to auto-switch and get margin or deficit vs threshold.
All four basic inputs are required. Advanced parameters are optional — defaults (13 dB SNR threshold, 3 dB NF, 6 dB losses, single pulse, monostatic) reflect typical textbook screening assumptions.
Inputs & Outputs
Inputs
Basic Inputs (Required)
- •Transmitted Power (P_t) — Peak power for pulsed radars; average power for CW/FMCW. Units: W, kW, MW, dBW, dBm. Typical ranges — marine 4–25 kW; ATC 1–5 MW peak; automotive 10 mW–1 W; weather 250 kW–1 MW.
- •Operating Frequency (f) — Carrier frequency from which wavelength λ = c/f is derived. Units: MHz or GHz. IEEE 521 bands: L 1–2, S 2–4, C 4–8, X 8–12, Ku 12–18, Ka 27–40, W 75–110 GHz.
- •Antenna Gain (G) — Gain over isotropic (dBi) or as a linear ratio. In monostatic configuration the same antenna serves transmit and receive, so G enters the range equation squared. Marine 25–32 dBi; ATC 33–40 dBi; high-gain dish 45–50 dBi.
- •Target RCS (σ) — Radar cross-section of the target. Units: m² or dBsm. Reference values — insect 10⁻⁵ m² (−50 dBsm); bird 0.01 m²; person 1 m²; fighter 1–6 m²; airliner 50–100 m²; cargo ship 10,000 m².
Advanced Inputs — Mode & Range
- •Calculation Mode — auto (default): mode is inferred from which range field is filled — design-verification takes priority over snr-at-range over max-range. Select explicitly to override inference.
- •Detection SNR Threshold (dB) — Required SNR at the detection boundary. Default 13 dB is a standard textbook screening value. Actual threshold depends on Pd, Pfa, target fluctuation model, and detector design.
- •Target Range (R_target) — Target distance for SNR-at-range mode. Filling this field with Mode=auto activates snr-at-range. Units: m, km, nmi.
- •Required Range (R_required) — Required detection distance for design-verification mode. Calculator reports SNR margin or deficit vs threshold. Filling this with Mode=auto activates design-verification. Units: m, km, nmi.
Advanced Inputs — Receiver & Waveform
- •Pulse Width (τ) — Transmitted pulse duration. Used to estimate receiver noise bandwidth as B ≈ 1/τ when Bandwidth field is blank. Units: ns, μs, ms.
- •Receiver Bandwidth (B) — Receiver noise bandwidth used in noise power calculation N = k·T·B·F. Defaults to 1/τ when pulse width is provided; otherwise defaults to 1 MHz with a notice. Units: kHz, MHz, GHz.
- •Noise Figure (NF, dB) — System noise figure referenced to 290 K per IEEE 686. Default 3 dB reflects a good LNA front-end. Uncooled receivers typically 4–8 dB.
- •Reference Temperature (T_ref, K) — Reference temperature for thermal noise calculation N = k·T·B·F. Default 290 K per IEEE 686. Do not raise T_ref while keeping NF active — this double-counts receiver noise.
- •System Losses (L_sys, dB) — Total system losses: transmit/receive path, radome, beam-shape (typical 1.6 dB), implementation loss. Default 6 dB. Excludes integration loss and atmospheric loss.
- •Atmospheric Attenuation Rate (dB/km) — Clear-air one-way attenuation rate. Round-trip loss = 2 × rate × R_km. When set, R_max becomes implicit and is solved iteratively. X-band ≈ 0.01 dB/km; Ka-band 0.1–0.5; W-band several dB/km.
Advanced Inputs — Configuration & Geometry
- •Configuration — Monostatic: single antenna for transmit and receive, G² in range equation. Bistatic: separate TX/RX antennas at different locations; activates Receive Gain, Bistatic Receive Range fields.
- •Receive Antenna Gain (G_r) — Bistatic only — gain of the receive antenna. Defaults to transmit gain G if left blank. Units: dBi or linear ratio.
- •Bistatic Receive Range (R_r) — Bistatic only — distance from target to receiver. Defaults to transmit-to-target range for symmetric geometry. Units: m, km, nmi.
- •Pulses Integrated (N) — Number of pulses integrated before threshold test. Default 1 (single pulse). Values >1 model integration gain.
- •Integration Type — Coherent: 10·log(N) dB gain (requires phase stability across the dwell). Non-coherent: conservative screening approximation G_int ≈ 10·log(N) − [2 + 1.5·log(N)] dB.
- •TX Antenna Height (h_t, m) — Transmit antenna height above surface for radio horizon estimate R_horizon ≈ 4.12·(√h_t + √h_r) km. Provide with h_r to activate horizon limiting.
- •RX Antenna Height (h_r, m) — Receive antenna height. When both h_t and h_r are provided, effective range is reported as min(R_max, R_horizon).
Outputs
Status Classification
- •Radar Status (Track A) — Primary compliance status: NORMAL (link feasible), EXTREME-RANGE (R_max > 5,000 km — sanity flag), INSUFFICIENT-RANGE (design target missed), or INFEASIBLE (invalid inputs).
- •Range Regime (Track B) — Operational regime: SHORT-RANGE (<10 km), MEDIUM-RANGE (10–100 km), LONG-RANGE (100–1,000 km), or VERY-LONG-RANGE (≥1,000 km). Combined badge reads e.g. NORMAL / MEDIUM-RANGE.
Primary Results
- •Wavelength (λ) — Derived from λ = c/f = 299,792,458 / f_Hz. Reported in cm. X-band 9.4 GHz → λ = 3.19 cm.
- •Maximum Range — Noise-limited detection range at the chosen SNR threshold. Reported in km. In design-verification mode, also compared against R_required. When horizon heights are set, min(R_max, R_horizon) is the effective range.
- •Maximum Range (nmi) — Same maximum detection range converted to nautical miles (1 nmi = 1.852 km).
- •EIRP — Effective isotropic radiated power = P_t × G_linear. Reported in dBW. A 25 kW radar with a 30 dBi antenna has 25 MW EIRP (+74 dBW). Used for spectral and EMI assessment.
- •Min Detectable Signal (MDS) — Minimum received power for detection = N × 10^(SNR_threshold/10). Reported in dBm. Sets the sensitivity floor of the radar.
- •Noise Power — Thermal noise at receiver input N = k_B · T_ref · B · F_n. Reported in dBm. At 290 K, 1 MHz bandwidth, 3 dB NF: approximately −108 dBm.
- •SNR — Signal-to-noise ratio at the computed or entered range. In max-range mode equals the SNR threshold. In snr-at-range mode reflects actual SNR at R_target. Reported in dB.
- •SNR Margin — SNR − SNR_threshold. Positive value means design has margin; negative means the required range is not achievable with current parameters. Active in design-verification mode. Reported in dB.
- •Calculation Mode — Resolved mode actually used: max-range, snr-at-range, or design-verification. Confirms which mode was inferred when Calculation Mode is set to auto.
Formula
Radar Range Equation
All calculations run internally in SI base units (W, Hz, m, m², K, s).
Wavelength
λ = c / f
where c = 299,792,458 m/s.
Monostatic Radar Range Equation
P_r = (P_t · G² · λ² · σ) / ((4π)³ · R⁴ · L_total)
where L_total = L_sys_linear × L_atm_rt_linear.
Bistatic Radar Range Equation
P_r = (P_t · G_t · G_r · λ² · σ) / ((4π)³ · R_t² · R_r² · L_total)
Noise Power
N = k_B · T_ref · B · F_n
where k_B = 1.38065 × 10⁻²³ J/K, F_n = 10^(NF_dB / 10).
Minimum Detectable Signal
MDS = N · 10^(SNR_threshold_dB / 10)
EIRP
EIRP = P_t · G_linear
EIRP_dBW = P_t_dBW + G_dBi
Maximum Detection Range
R_max = [P_t · G² · λ² · σ / ((4π)³ · MDS_eff · L_total)]^(1/4)
When L_atm_rate is provided, R_max is implicit (L_total depends on R). The calculator iterates until |R_{n+1} − R_n| / R_n < 0.1%.
Pulse Integration Gain
Coherent:
G_int_coh_dB = 10 · log₁₀(N_pulses)
Non-coherent (screening approximation):
G_int_nc_dB = 10 · log₁₀(N_pulses) − [2 + 1.5 · log₁₀(N_pulses)]
Radio Horizon
R_horizon_km = 4.12 · (√h_t_m + √h_r_m)
Factor 4.12 includes 4/3 effective Earth radius for standard atmosphere.
Track A Status Priority
| Priority | Status | Condition |
|---|---|---|
| 0 | INFEASIBLE | Required input ≤ 0 |
| 1 | EXTREME-RANGE | R_max > 5,000 km |
| 2 | INSUFFICIENT-RANGE | Design Verification + SNR < threshold |
| 3 | NORMAL | All checks pass |
Track B Range Regime
| Class | Condition |
|---|---|
| SHORT-RANGE | R < 10 km |
| MEDIUM-RANGE | 10 km ≤ R < 100 km |
| LONG-RANGE | 100 km ≤ R < 1,000 km |
| VERY-LONG-RANGE | R ≥ 1,000 km |
What is the Radar Range Equation
The radar range equation predicts how far a radar can detect a target by tracking energy flow from transmitter to target and back to receiver. Power leaves the antenna concentrated into a narrow beam, spreads geometrically over a hemisphere centered on the target, reflects off the target with a strength characterized by its radar cross-section, spreads again over a hemisphere centered on the radar, and arrives at the receiving antenna.
Each spreading step introduces a 1/R² factor for spherical wave expansion. The round trip therefore produces 1/R⁴ in the received power. This is the dominant scaling of radar range performance. Cutting the detection range requirement in half eases the required transmitter power by a factor of 16. Doubling the detection range demands 16 times the transmitter power, antenna aperture squared, target RCS, or any combination that multiplies to 16.
The equation is noise-limited. It predicts the range at which the received signal from the target exceeds the receiver thermal noise floor by the chosen SNR threshold. Real radar performance is also bounded by clutter, multipath, target fluctuation, atmospheric anomalies, and signal processing losses — none of which are part of the basic range equation.
The form used here assumes a point target with frequency-independent RCS, free-space propagation with optional uniform atmospheric attenuation, a matched-filter receiver, and thermal noise as the only noise source. These assumptions are appropriate for first-order sizing and textbook problems. They break down for distributed targets (weather, clutter), low-grazing-angle geometries, and atmospheric anomaly conditions.
Monostatic Radar Range Equation
The monostatic radar range equation describes a radar in which the same antenna handles transmission and reception. The same antenna gain enters the equation on both legs of the round trip, producing the characteristic G² dependence.
The received power from a point target at range R:
P_r = (P_t · G² · λ² · σ) / [(4π)³ · R⁴ · L_total]
where P_t is transmitted power (W), G is antenna gain over isotropic (linear), λ is wavelength (m), σ is target radar cross-section (m²), R is range to target (m), and L_total is the combined linear loss including system losses and round-trip atmospheric attenuation.
Solving for the maximum range gives:
R_max = [P_t · G² · λ² · σ / ((4π)³ · MDS_eff · L_total)]^(1/4)
The fourth root makes range trade-offs gentle: a 16-fold increase in any numerator term doubles R_max. The G² dependence makes antenna gain the strongest lever in monostatic radar design. Adding 6 dB of antenna gain (a factor of 4 in linear gain) gives 16 times the received power, doubling the range. Doubling only the transmitter power adds only 19% range.
Bistatic Radar Range Equation
The bistatic radar range equation handles configurations with separate transmit and receive antennas. The transmit antenna illuminates the target from one location; a different antenna at another location receives the scattered signal. The two propagation paths are independent, so the equation uses the product of the two range factors rather than R⁴.
P_r = (P_t · G_t · G_r · λ² · σ) / [(4π)³ · R_t² · R_r² · L_total]
For symmetric geometry (R_t = R_r = R), the spreading-loss term is R⁴ — identical to monostatic. Asymmetric geometries enable interesting trade-offs: a high-gain transmit antenna can illuminate at long range while a more modest receive antenna closer to the target captures the return.
The critical caveat is bistatic RCS. The σ in the bistatic equation is the bistatic radar cross-section, which depends on the bistatic angle (the angle subtended at the target between transmit and receive directions) and can vary by tens of dB from the monostatic value. The calculator uses the entered σ unchanged with an explicit notice.
Maximum Radar Detection Range
The maximum radar detection range R_max is the distance at which received signal power from the target equals the minimum detectable signal power at the chosen SNR threshold. Beyond R_max, the signal falls below the detection threshold.
The fourth-root relationship makes R_max relatively insensitive to small changes in individual parameters. A 1 dB optimistic loss estimate inflates R_max by only about 6%. Closing a detection-range gap requires substantial parameter changes — extending R_max by 50% needs a 5-fold increase in transmitted power, antenna gain squared, or target RCS, or any combination that multiplies to 5.
R_max depends on the chosen SNR threshold and integration settings. The default 13 dB threshold is a screening value. Different applications use different thresholds: strategic surveillance may use 6–10 dB with extensive integration, while precision tracking may demand 16–20 dB on a single look.
Integration gain raises R_max by easing the effective threshold. Ten pulses non-coherent gives about 6.5 dB of integration gain (screening estimate), reducing the effective single-pulse threshold from 13 dB to 6.5 dB. Coherent integration scales as 10·log(N) and gives larger gains but demands phase stability across the dwell.
EIRP vs Transmitter Power
Transmitter power P_t is the raw power the radar generates at the output of the final stage. Effective isotropic radiated power (EIRP) is the power density in the antenna boresight direction expressed as the equivalent isotropic radiator power:
EIRP = P_t · G_linear
EIRP_dBW = P_t_dBW + G_dBi
A 25 kW marine radar with a 30 dBi (linear gain 1,000) antenna has 25 MW of EIRP. The radar does not actually radiate 25 MW — it generates 25 kW and the antenna concentrates that power into a narrow beam.
Confusing P_t with EIRP is one of the most common errors in radar calculations. Using P_t = 25 MW (instead of 25 kW) when solving the range equation overestimates the received power by a factor of 1,000 and inflates R_max by 1,000^(1/4) ≈ 5.6. Conversely, using EIRP in place of P_t · G² double-counts the antenna gain.
EIRP matters for spectrum regulation, EMI assessment, and RF exposure limits. The calculator reports EIRP as a primary output in both linear and dBW form. ERP (referenced to a half-wave dipole) sits 2.15 dB lower than EIRP.
RCS and dBsm Explained
Radar cross-section σ is the equivalent area that, if it captured all incident radar power and reradiated it isotropically, would produce the same received signal as the actual target. RCS has units of area — square meters in SI.
The logarithmic form is decibel-square-meters: σ_dBsm = 10·log₁₀(σ_m²).
Reference RCS values:
- −50 dBsm (10⁻⁵ m²): Small insect
- −20 dBsm (0.01 m²): Bird, small UAV
- 0 dBsm (1 m²): Person, small missile
- +10 dBsm (10 m²): Large fighter aircraft, small boat
- +20 dBsm (100 m²): Commercial airliner
- +40 dBsm (10,000 m²): Cargo ship
R_max scales as σ^(1/4). A 10× reduction in RCS (−10 dB) reduces R_max by 10^(1/4) ≈ 1.78. A 100× reduction (−20 dB) reduces R_max by 100^(1/4) ≈ 3.16. To cut detection range by 10×, RCS must reduce by 10⁴ = 40 dB — which explains why effective stealth requires extremely low RCS values.
RCS varies strongly with aspect angle (20–40 dB swings), frequency, and geometry. Real detection analysis uses Swerling fluctuation models rather than a single RCS value. The calculator uses a single σ as a screening proxy, and fires LOW-RCS-NOTICE when σ falls below 0.1 m² (−10 dBsm) and VERY-LOW-RCS-WARNING below 0.001 m² (−30 dBsm).
Radio Horizon vs Radar Equation Range
The radar range equation gives the noise-limited propagation range. The radio horizon gives the geometric line-of-sight range. The actual detection range is the smaller of the two.
For standard atmosphere with 4/3 effective Earth radius:
R_horizon_km ≈ 4.12 · (√h_t_m + √h_r_m)
A 30 m (98 ft) radar tower watching a 30 m mast reaches:
R_horizon ≈ 4.12 · (√30 + √30) ≈ 45 km (24 nmi)
A 100 m tower watching a 10 m target:
R_horizon ≈ 4.12 · (√100 + √10) ≈ 54 km (29 nmi)
For airborne platforms at 10,000 m altitude watching a 100 m target:
R_horizon ≈ 4.12 · (√10000 + √100) ≈ 453 km (245 nmi)
The calculator computes R_horizon when both antenna heights are provided and reports the effective range as min(R_max, R_horizon). The HORIZON-LIMITED-NOTICE fires when the propagation-limited range exceeds the horizon.
Non-standard atmospheres modify the picture. Anomalous ducting can extend ranges far beyond the formula. Sub-refraction shortens the apparent horizon. Ionospheric refraction at HF and VHF enables over-the-horizon propagation through different physics. None of these effects are modeled.
Radar Range Scaling Rules
Quick mental models from R_max ∝ (P_t · G² · σ / L)^(1/4):
- 2× range requires 16× power, gain squared, or RCS
- +6 dB transmit power gives 1.41× range
- +12 dB SNR margin gives 2× range
- 10× target RCS gives 1.78× range
- +3 dBi antenna gain (monostatic) gives +6 dB SNR margin and 1.41× range — antenna enters twice
- +3 dB noise figure cuts range by 16% (R ∝ NF^(−1/4))
- +6 dB system loss cuts range by 30%
- 4× coherent pulse integration gives +6 dB and 1.41× range
- Cutting range in half raises SNR by 12 dB
FAQ
How do I calculate maximum radar detection range?
Enter transmitted power, antenna gain, frequency, and target RCS in the four basic fields and click Calculate. With default SNR threshold (13 dB), noise figure (3 dB), and system losses (6 dB), the maximum range appears immediately. The result follows R_max = [P_t · G² · λ² · σ / ((4π)³ · MDS · L)]^(1/4). A factor of 16 in any numerator term doubles the range.
What is EIRP and how does it differ from transmitter power?
Transmitter power P_t is what the radar generates at the output stage. EIRP = P_t × G, where G is the linear antenna gain. A 25 kW transmitter with a 30 dBi antenna has 25 MW of EIRP. The radar concentrates 25 kW so the boresight power density matches an isotropic 25 MW source. ERP referenced to a half-wave dipole is 2.15 dB lower than EIRP.
How does antenna gain affect radar range in monostatic configuration?
Antenna gain appears squared in monostatic. A 3 dBi increase (linear factor of 2) gives +6 dB in received signal and 1.41× range. Adding 6 dBi of antenna gain quadruples received power and doubles R_max. This makes antenna aperture the single strongest dB-per-dB design lever for monostatic radar.
What is dBsm and how do I convert RCS values?
σ_dBsm = 10·log₁₀(σ_m²). A 1 m² target is 0 dBsm. A 100 m² airliner is +20 dBsm. A 0.01 m² bird is −20 dBsm. R_max scales as σ^(1/4): a 100× RCS reduction cuts range by only 3.16×. The calculator accepts both forms.
Why does atmospheric loss enter as 2 × rate × range?
The signal traverses the atmosphere twice — once to the target and once back. For a constant rate, L_atm_round_trip = 2 × rate × R_km. This makes R_max implicit when L_atm_rate is set, so the calculator iterates until the relative change is below 0.1%, typically in 3–5 iterations.
What is the radio horizon and when does it limit detection?
R_horizon (km) ≈ 4.12 × (√h_t + √h_r) with heights in meters. A 30 m tower watching a 30 m mast reaches about 45 km (24 nmi). The calculator reports effective range as min(R_max, R_horizon) when both heights are entered. Targets beyond the horizon are geometrically shadowed regardless of radar performance.
Why does my marine radar specification show a longer range than this calculator gives?
Marketed ranges assume larger reference targets, longer pulses, pulse integration, better noise figures (1–2 dB vs 3 dB default), and lower system losses. Adjust the defaults to match the specification's assumptions and the numbers align.
Can I use this calculator for weather radar or automotive FMCW radar?
For weather radar, no — distributed scatterers follow the volume radar equation with reflectivity factor Z. For automotive FMCW, the calculator gives a received-power estimate only, not chirp processing, range FFT, Doppler FFT, or CFAR. Use it as a starting point for the power-link portion.
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Key Facts
- Received power drops as the fourth power of range — doubling detection range demands a factor of 16 in transmitted power, antenna gain squared, target RCS, or some combination.
- In monostatic radar, antenna gain appears squared because the same antenna serves both transmit and receive. Adding 6 dBi of antenna gain quadruples received power and doubles R_max.
- EIRP is P_t × G referenced to an isotropic radiator. A 25 kW marine radar with a 30 dBi antenna has 25 MW of EIRP — not 25 kW.
- The default 13 dB SNR threshold is a screening value. Actual detection depends on Pd, Pfa, integration, target fluctuation, and detector design.
- At 290 K with 1 MHz bandwidth and 3 dB NF, the thermal noise floor is approximately −138 dBW (−108 dBm). Detection at 13 dB requires received power above −125 dBW.
- Atmospheric loss matters above C-band. X-band loses ≈ 0.01 dB/km clear-air; Ka-band 0.1–0.5 dB/km; W-band several dB/km. Rain dominates K through W band.
- Radio horizon R_horizon (km) ≈ 4.12 × (√h_t + √h_r) with heights in meters. A 30 m mast watching a 30 m mast reaches ≈ 45 km (24 nmi).
- Bistatic RCS is not monostatic RCS. Real bistatic σ varies with the bistatic angle and can differ from monostatic by tens of dB.
- Non-coherent integration of 10 pulses gives about 6.5 dB gain (screening estimate), reducing the effective SNR threshold from 13 dB to 6.5 dB.
- A 100× (−20 dB) reduction in target RCS reduces R_max by 100^(1/4) ≈ 3.16 — the σ^(1/4) scaling explains why stealth shaping must achieve very low RCS to meaningfully shrink detection volumes.
Applications
- Air traffic control primary surveillance radar sizing (S-band, 1–5 MW, 33–40 dBi, 60–80 nmi coverage).
- Marine navigation radar performance verification (X-band, 4–25 kW, SOLAS minimum detection requirement).
- Automotive radar link estimates at 76–81 GHz (free-space power link only, not chirp processing).
- Military air defense and stealth target detection range trade studies.
- Weather radar point-target screening (not distributed-scatterer dBZ analysis).
- Ground-based early warning radar noise-limited range estimation.
- Bistatic and passive radar geometry studies.
- Textbook problem verification and radar course education.
- Pulse integration benefit analysis (coherent vs non-coherent).
- Design verification — checking whether a proposed radar system meets a required detection range.
Example Calculation
Example: Marine X-band Navigation Radar (Max-Range Mode)
Inputs:
- Transmitted power: 25 kW
- Frequency: 9.4 GHz (X-band)
- Antenna gain: 30 dBi
- Target RCS: 100 m² (cargo ship)
- SNR threshold: 13 dB
- Pulse width: 0.5 μs
- Mode: auto (both range fields blank → max-range)
- All other: default (NF = 3 dB, T_ref = 290 K, L_sys = 6 dB)
Step 1 — Wavelength:
λ = 299,792,458 / (9.4 × 10⁹) = 0.0319 m = 3.19 cm
Step 2 — Receiver bandwidth:
B = 1 / 0.5μs = 2 MHz
Step 3 — EIRP:
G_linear = 10^(30/10) = 1,000
EIRP = 25,000 × 1,000 = 25 MW (+74.0 dBW)
Step 4 — Noise power:
N = 1.38×10⁻²³ × 290 × 2×10⁶ × 10^(3/10)
≈ 1.60 × 10⁻¹⁴ W (−138.0 dBW, −108.0 dBm)
Step 5 — MDS at 13 dB:
MDS = 1.60×10⁻¹⁴ × 10^(13/10) ≈ 3.19 × 10⁻¹³ W
≈ −124.97 dBW ≈ −95.0 dBm
Step 6 — R_max:
Numerator = 25,000 × 10⁶ × (0.0319)² × 100 ≈ 2.54 × 10⁹
Denominator = (4π)³ × 3.19×10⁻¹³ × 3.981 ≈ 2.52 × 10⁻⁹
R_max⁴ ≈ 1.0 × 10¹⁸
R_max ≈ 31.7 km (17.1 nmi)
Status: Track A = NORMAL, Track B = MEDIUM-RANGE Combined badge: NORMAL / MEDIUM-RANGE
Standards & References
- IEEE Std 686-2017 — Radar Definitions. Authoritative terminology for range equation terms, antenna gain conventions, noise figure, RCS, and detection.
- IEEE Std 521-2019 — Standard Letter Designations for Radar-Frequency Bands. Defines L, S, C, X, Ku, K, Ka, V, W band designations.
- ITU-R P.676-13 — Attenuation by Atmospheric Gases and Related Effects (08/2022). Reference for atmospheric gas attenuation rates.
- ITU-R V.431 — Nomenclature of frequency and wavelength bands.
- Skolnik, M. I. — Introduction to Radar Systems, 3rd ed. (McGraw-Hill, 2001). Most-cited reference for radar fundamentals.
- Richards, M. A. — Fundamentals of Radar Signal Processing, 3rd ed. (McGraw-Hill, 2022). Signal-processing reference.
- Mahafza, B. R. — Radar Systems Analysis and Design Using MATLAB, 4th ed. (CRC Press, 2022). Working examples.
- Stimson, G. W. — Introduction to Airborne Radar, 3rd ed. (SciTech, 2014). Airborne and pulse-Doppler focus.
Limitations
- Produces the noise-limited range only. Does not model clutter (ground, sea, weather), external interference, or jamming.
- Treats the target as a point scatterer with a single constant RCS. Real targets show 20–40 dB aspect-angle variation and frequency dependence.
- The SNR threshold does not correspond to a specific Pd/Pfa combination. Detection probability analysis requires target fluctuation models and detector design.
- Pulse compression is not modeled. For LFM chirp and other coded waveforms, enter the receiver bandwidth directly.
- FMCW processing gain is not modeled — range FFT, Doppler FFT, CFAR, and MIMO beamforming are outside the equation.
- Atmospheric loss is modeled as a constant dB/km rate. Real attenuation varies with altitude, water vapor, rain rate, and frequency per ITU-R P.676.
- Bistatic mode assumes the entered σ equals the bistatic RCS. Real bistatic σ varies with the bistatic angle and can differ by tens of dB.
- Radio horizon formula uses 4/3 effective Earth radius for standard atmosphere. Ducting and ionospheric effects are not modeled.
- Integration gain for non-coherent integration is a conservative screening approximation — actual gain depends on Pd, Pfa, and detector implementation.
- The 5,000 km EXTREME-RANGE threshold is a sanity flag. Strategic early-warning and OTH radars require different propagation models.
Common Mistakes to Avoid
- Confusing EIRP with transmitter power — a 25 kW radar with a 30 dBi antenna has 25 MW of EIRP, not 25 kW. Using EIRP instead of P_t in the range equation double-counts antenna gain.
- Entering power in wrong units — a 1 MW transmitter typed as 1 W gives an R_max 31.6 times shorter than the correct value. Check the unit dropdown.
- Using average power for a pulsed radar — matched-filter detection processes peak power during the pulse. Using average power for a low-duty-cycle radar significantly underestimates detection range.
- Forgetting that antenna gain appears twice in monostatic — 3 dBi of additional antenna gain (factor of 2 linear) gives +6 dB SNR and 1.41× range, not +3 dB.
- Treating bistatic RCS as monostatic RCS — bistatic σ varies with bistatic angle. Using a monostatic measurement in bistatic mode can give errors of tens of dB.
- Ignoring atmospheric loss above C-band — X-band loses 1 dB over 50 km clear-air; Ka-band 5–25 dB over 50 km. Ignoring this inflates R_max non-trivially at long range.
- Adjusting T_ref while keeping NF active — NF is referenced to 290 K by convention. Raising T_ref while leaving NF unchanged double-counts receiver noise.
- Using the 13 dB threshold as a specific Pd/Pfa — it is a screening value. Swerling I targets may need 20 dB for Pd ≈ 0.5 at Pfa = 10⁻⁶.
- Comparing marketed marine radar range with the screening result without matching assumptions — marketed 48 nmi ranges often assume larger reference targets, better NF, longer pulses, and pulse integration.
- Using the point-target equation for weather radar — distributed scatterers follow the volume radar equation with reflectivity factor Z; the point-target form gives meaningless dBZ results.
Frequently Asked Questions
How do I calculate maximum radar detection range?
What is EIRP and how does it differ from transmitter power?
How does antenna gain affect radar range in monostatic configuration?
What is dBsm and how do I convert RCS values?
Why does atmospheric loss enter as 2 × rate × range?
What is the radio horizon and when does it limit detection?
Why does my marine radar specification show a longer range than this calculator gives?
Can I use this calculator for weather radar or automotive FMCW radar?
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Peak power for pulsed radars, average for CW/FMCW. Marine 4–25 kW; ATC 1–5 MW peak; automotive 10 mW–1 W.
IEEE 521 bands: L 1–2; S 2–4; C 4–8; X 8–12; Ku 12–18; Ka 27–40; W 75–110 GHz.
Gain over isotropic. Marine 25–32 dBi; ATC 33–40 dBi; high-gain dish 45–50 dBi.
Insect −50 dBsm; bird −20 dBsm; person 0 dBsm; fighter +5 dBsm; airliner +20 dBsm; cargo ship +40 dBsm.
Mode selection, range targets, pulse width and bandwidth, noise figure and temperature, system and atmospheric losses, configuration, pulse integration, antenna heights (all optional — defaults handle typical screening).