Radar Resolution Calculator | Range, Velocity & Angle

What Does a Radar Resolution Calculator Do?

A radar resolution calculator takes your system parameters—signal bandwidth, coherent processing interval (CPI) and antenna aperture—and returns the minimum separable distance, velocity and angle between two targets. Range resolution depends on bandwidth, velocity resolution on dwell time and carrier frequency, and angular resolution on aperture size relative to wavelength. The tool below computes all three so you can evaluate trade-offs in a single step.

Range Resolution: Why Bandwidth Rules

Range resolution (ΔR) is the ability to distinguish two targets at different distances along the same line of sight. The governing equation is straightforward:

ΔR = c / (2 × B)

where c is the speed of light (≈ 3 × 10⁸ m/s) and B is the transmitted signal bandwidth in Hz. A 1 GHz bandwidth yields ΔR = 0.15 m (15 cm); a 4 GHz bandwidth—common in 77 GHz automotive FMCW radars—pushes that down to about 3.75 cm. No amount of processing gain or antenna refinement can improve range resolution beyond what bandwidth allows.

For a deeper look at the physics and PCB-level implications of wideband radar signals, see our guide to radar range resolution and bandwidth.

Practical Bandwidth Limits

Regulatory allocations set the ceiling. The 76–77 GHz automotive band gives 1 GHz of bandwidth (ΔR ≈ 15 cm), while the 77–81 GHz band opens 4 GHz (ΔR ≈ 3.75 cm). In X-band (9.0–9.5 GHz) marine radar you have only 500 MHz, so ΔR ≈ 30 cm at best. PCB trace and laminate losses grow with bandwidth; a 4 GHz chirp at 79 GHz on Rogers RO3003 (Dk 3.00, Df 0.0010 at 10 GHz) still needs careful stackup control to keep insertion loss under 0.15 dB/mm at millimeter-wave frequencies.

Velocity Resolution: Dwell Time and Carrier Frequency

Velocity resolution (Δv) determines the minimum speed difference you can separate between two co-range targets. It is set by the coherent processing interval (T_CPI) and the carrier frequency (f_c):

Δv = λ / (2 × T_CPI) = c / (2 × f_c × T_CPI)

At 77 GHz with a CPI of 10 ms, Δv ≈ 0.19 m/s—adequate for separating pedestrians from vehicles. Halving the CPI doubles Δv, so there is a direct trade-off between velocity resolution and frame rate. Our article on radar velocity resolution and Doppler ambiguity covers the aliasing and unambiguous velocity limits you need to manage alongside resolution.

Connecting Doppler Shift to Resolution

Velocity resolution is really frequency resolution in the Doppler domain. The minimum resolvable Doppler shift is 1/T_CPI, and velocity maps to Doppler via f_d = 2v/λ. If you need to verify Doppler-shift values for a specific target speed, our Doppler shift calculator converts velocity to frequency shift directly.

Angular Resolution: Aperture and Wavelength

Angular resolution (Δθ) describes the minimum angular separation at which two targets appear as distinct returns. For a uniformly illuminated aperture of dimension D:

Δθ ≈ λ / D (radians)

or roughly 0.886 λ/D for a uniformly weighted linear array (the 0.886 factor accounts for the −3 dB beamwidth of a sinc pattern). At 77 GHz (λ ≈ 3.9 mm), a 12-element patch array with half-wavelength spacing spans about 23.4 mm, giving Δθ ≈ 0.886 × 3.9 / 23.4 ≈ 0.148 rad ≈ 8.5°. Doubling the aperture to 24 elements halves the beamwidth to about 4.2°.

Phased arrays can steer this beam electronically. To compute the required inter-element phase taper for a given scan angle, use the phased array beam steering calculator.

Aperture Trade-offs on the PCB

A larger aperture improves angular resolution but increases board area, layer count and cost. A 24-element, 77 GHz patch array on a 4-layer RO3003 stackup might occupy 25 × 50 mm, while a 48-element virtual-MIMO array on TI’s AWR2243 cascaded architecture can synthesize 86 virtual channels on a board under 60 × 60 mm. Routing the IF and LO distribution networks across that area without coupling into the antenna feed demands careful ground-plane stitching and controlled-impedance lines—factors you can prototype quickly with the RF PCB stackup builder.

The Radar Resolution Calculator

Enter your signal bandwidth (MHz or GHz), carrier frequency, coherent processing interval and antenna aperture dimension below. The calculator returns range resolution in meters and centimeters, velocity resolution in m/s, and angular resolution in degrees.

For a worked example: a 77 GHz FMCW radar with 4 GHz bandwidth, 20 ms CPI and a 40 mm aperture yields ΔR = 3.75 cm, Δv ≈ 0.097 m/s and Δθ ≈ 4.9°. If ΔR is sufficient but Δθ is too coarse for your lane-separation requirement, the calculator shows immediately that you need a wider aperture or more array elements—not more bandwidth. That kind of quick trade-off analysis is exactly what saves design iterations.

How the Three Resolutions Interact in System Design

No single knob improves all three simultaneously without penalty. Increasing carrier frequency from 24 GHz to 77 GHz shrinks λ by 3.2×, which helps angular resolution for the same aperture, but the shorter wavelength also raises free-space path loss and PCB dielectric loss. A full link-budget check with the radar link budget calculator confirms whether your SNR margin survives the move to a higher band.

Choosing Parameters for Common Radar Applications

Automotive Short-Range Radar (77–81 GHz)

• Bandwidth: 2–4 GHz → ΔR = 3.75–7.5 cm
• CPI: 10–30 ms → Δv = 0.065–0.19 m/s
• Aperture: 30–60 mm → Δθ = 3–7°
• PCB note: RO3003 or Megtron 7 for low Df at 79 GHz; 4–6 layer stackup with embedded patch elements.

Marine Navigation Radar (X-band, 9.4 GHz)

• Bandwidth: 25–50 MHz (magnetron) → ΔR = 3–6 m
• CPI: Pulse-to-pulse (non-coherent) → velocity resolution via scan-to-scan tracking, not Doppler
• Aperture: 0.6–1.8 m slotted waveguide → Δθ = 1–3°

UAV Sense-and-Avoid (24 GHz ISM)

• Bandwidth: 250 MHz → ΔR = 60 cm
• CPI: 5–10 ms → Δv = 0.6–1.25 m/s
• Aperture: 50–100 mm → Δθ = 7–14°
• PCB note: Standard RO4350B (Dk 3.48, Df 0.0037) is cost-effective at 24 GHz; two-layer or four-layer builds keep weight under 10 g for small UAV modules.

Common Pitfalls

• Confusing resolution with accuracy. Resolution is the ability to separate two targets; accuracy is how close a measured position is to truth. You can have 15 cm range resolution but sub-centimeter range accuracy via interpolation.
• Ignoring windowing effects. Applying a Hanning or Chebyshev window to the FFT broadens the main lobe by 1.4–1.7× compared to a rectangular window, degrading both range and velocity resolution by the same factor.
• Neglecting PCB loss at wide bandwidths. A 4 GHz chirp at 79 GHz can lose 2–3 dB in a 15 mm microstrip feed if the laminate Df exceeds 0.004. That loss directly reduces SNR and detection range—check it against your link budget.
• Assuming angular resolution equals angular accuracy. Monopulse or digital beamforming can measure angle to a fraction of a beamwidth, but two unresolved targets within one beamwidth still merge into a single return.

FAQ

What is the formula for radar range resolution?

Range resolution ΔR = c / (2B), where c is the speed of light and B is the signal bandwidth. A 1 GHz bandwidth gives 15 cm range resolution regardless of carrier frequency.

Does higher carrier frequency improve range resolution?

No. Range resolution depends only on bandwidth, not carrier frequency. A 24 GHz radar with 1 GHz bandwidth has the same 15 cm range resolution as a 77 GHz radar with 1 GHz bandwidth. Higher frequency helps angular resolution for a given aperture size.

How do I improve velocity resolution without increasing CPI?

You can raise the carrier frequency (shorter λ makes the same CPI yield finer Δv), use a higher-order spectral estimator like MUSIC or ESPRIT instead of a standard FFT, or accept a coarser frame rate and lengthen the CPI. There is no free lunch—each approach has cost or complexity trade-offs.

What PCB material is best for wideband radar?

For bandwidths above 2 GHz at millimeter-wave frequencies, low-loss PTFE laminates like Rogers RO3003 (Df ≈ 0.0010 at 10 GHz) are the industry standard. Hydrocarbon-ceramic options like RO4835T offer a lower-cost alternative at 24 GHz where losses are less critical.

Can I calculate radar cross section alongside resolution?

Resolution tells you whether two targets are separable; RCS tells you how much energy each target reflects. They are independent parameters. Use the radar cross section calculator to estimate RCS for common target shapes and feed the result into a link-budget analysis.