Radar Resolution Calculator
Calculate radar range resolution, cross-range (azimuth) resolution, beam footprint, and equivalent reciprocal bandwidth from radar bandwidth, antenna beamwidth, and target distance.
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Inputs
Live
Math
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Related
Enter parameters and click Calculate to view results
Formula & Theory
ΔR = c/(2B), ΔAz ≈ (R·θ)/2, Beam Footprint ≈ R·θThis formula is used to calculate antenna parameters for radar resolution calculator.
Overview
The Radar Resolution Calculator evaluates key target-discrimination parameters, including slant-range resolution ($\Delta R$), cross-range (azimuth) resolution ($\Delta \text{Az}$), total 3 dB beam footprint width at a given range ($R$), and pulse reciprocal bandwidth ($1/B$).
Input Guide
Enter Signal Bandwidth (B), Antenna 3 dB Beamwidth (θ), Target Distance (R) exactly in the units shown by this radar resolution. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Signal Bandwidth (B) — use MHz.
- Antenna 3 dB Beamwidth (θ) — use deg.
- Target Distance (R) — use km.
Output Guide
The results describe the calculated radar resolution 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 Resolution uses ΔR = c/(2B), ΔAz ≈ (R·θ)/2, Beam Footprint ≈ R·θ. Supply Signal Bandwidth (B) (MHz), Antenna 3 dB Beamwidth (θ) (deg), Target Distance (R) (km) in the displayed units, then use the calculated values as the first engineering target for this radar engineering design or analysis.
Design Notes
Slant-range resolution depends strictly on signal bandwidth ($\Delta R = \frac{c}{2B}$) and is independent of target distance, whereas cross-range (angular) resolution worsens linearly with distance ($\Delta \text{Az} \approx \frac{R \cdot \theta}{2}$). High-resolution range imaging requires wideband waveforms or pulse compression (e.g., linear frequency modulation or chirp networks), while fine cross-range resolution at long distances demands electrically large antenna apertures, higher operating frequencies, or Synthetic Aperture Radar (SAR) processing.
Build and Tuning Notes
When configuring real-world radar architectures, windowing functions (e.g., Hamming, Taylor, or Hann weightings) applied to compressed pulses reduce range sidelobes at the expense of broadening the mainlobe pulse width (typically broadening range resolution by a factor of 1.2 to 1.5). Similarly, cross-range resolution calculations use the half-power (3 dB) beamwidth ($\theta_{3\text{dB}}$ in radians) as a primary approximation, but pulse integration and target monopulse tracking techniques can further refine angular location accuracy beyond the raw beam footprint.
Frequently Asked Questions
What is the difference between range resolution and cross-range resolution?
Range resolution ($\Delta R$) is the ability to separate two distinct targets located along the same line of sight (radial distance from the antenna). Cross-range (azimuth) resolution is the ability to resolve two targets located at the same distance but separated perpendicularly across the antenna beam.
How does signal bandwidth affect range resolution?
Range resolution is inversely proportional to signal bandwidth ($\Delta R = \frac{c}{2B}$). Higher bandwidth provides finer pulse duration after compression, allowing closer radial target separation. For example, a $100 \text{ MHz}$ bandwidth provides a range resolution of $1.5 \text{ m}$.
Does target range affect range resolution?
No. In free space, range resolution depends solely on the speed of light ($c$) and waveform bandwidth ($B$). It remains constant regardless of whether the target is $1 \text{ km}$ or $100 \text{ km}$ away.
How is cross-range (azimuth) resolution calculated?
Cross-range resolution at distance $R$ with half-power beamwidth $\theta$ (in radians) is given by $\Delta \text{Az} \approx \frac{R \cdot \theta}{2}$. The total width of the beam footprint at range $R$ is $R \cdot \theta$. Because angular beam divergence spreads over distance, cross-range resolution degrades linearly as range increases.
What is reciprocal bandwidth (1/B)?
Reciprocal bandwidth ($1/B$) represents the minimum effective pulse duration or compressed pulse width in time. For an unmodulated rectangular pulse, it equals the pulse width; for pulse-compressed waveforms (such as LFM chirps), it represents the duration of the output impulse response after matched filtering.
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.