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Radar resolution calculator

Radar resolution is the smallest separation at which two targets still show up as two echoes. Along the beam it is c·τ/2 for a plain pulse, or c/(2B) for a waveform of bandwidth B. Across the beam it is the width of the beam at that range, R·θ. This calculator gives both and the resolution cell they span.

A selection, read 7 November 2026. Marine: Furuno FAR-2117 with its 6.5 ft array (0.07 µs, 1.23°). NEXRAD: 0.96° with 1.57 or 4.57 µs, from Wikipedia. Automotive: a 4 GHz chirp (TI) with an illustrative 5 cm aperture at 77 GHz. Each preset also sets a typical range of this tool’s choosing.

Length of one unmodulated pulse. For a compressed pulse, switch to bandwidth.

°

The −3 dB beamwidth in the direction you want to resolve, usually horizontal.

Distance to the targets. It sets only the cross-range cell, because range resolution is the same at every distance.

Range resolution ΔR
149.9
c·τ/2, bandwidth ≈ 1/τ = 1 MHz
Cross-range resolution Δx
214.7
R·θ at 10 km
Beamwidth used θ
1.23 °
0.02147 rad
Resolution cell
32180
ΔR × Δx = 149.9 m × 214.7 m
  • A plain pulse has a bandwidth of about 1/τ = 1 MHz. Pulse-compression and FMCW radars sweep a wider band inside a long pulse and resolve c/(2B), so bandwidth is the real driver.
plan viewbeam angle ×11.4 · cell depth ×4.4radarR = 10 kmθ = 1.23°Δx = 214.7 mΔR = 149.9 m

Plan view from above. The radar sits on the left and the green fan is its half-power beam. The darker patch at range R is one resolution cell, ΔR deep and Δx wide. The two dots on the beam axis are point targets exactly ΔR apart, at the near and far edge of the cell. They are just resolved, and any closer they merge into one echo. Two targets side by side are resolved only when they are more than Δx apart. The beam angle and the cell depth are stretched or squeezed to stay readable, and the top line says by how much. ΔR and Δx use the unit you picked last.

Real-aperture resolution of a monostatic radar. Synthetic-aperture radar (SAR) and Doppler beam sharpening reach far finer cross-range cells and are not modelled. The cross-range figure is the arc R·θ of the half-power beam, and the 70·λ/D estimate assumes a dish-like aperture. Furuno is a trademark of Furuno Electric Co., Ltd. Waveshed is not affiliated with it.

How it works

  1. 01

    Range resolution from the pulse

    Two targets one behind the other return two echoes. If the echoes overlap in time, the radar sees one. The echo travels out and back, so targets closer than c·τ/2 along the beam merge into one. That is 150 m per microsecond of pulse.

  2. 02

    Bandwidth is the real driver

    A plain pulse has a bandwidth of about 1/τ, so c·τ/2 = c/(2B). Pulse-compression and FMCW radars sweep a wide band inside a long pulse. They keep the energy of the long pulse and resolve c/(2B). With 4 GHz of sweep that is 3.75 cm.

  3. 03

    Beamwidth from the antenna

    Type the half-power beamwidth from a datasheet, or let the page estimate it from the antenna size and frequency with θ ≈ 70·λ/D degrees. That is the same rule as the dish gain calculator (ITU-R F.699), about 1.22·λ/D in radians and good to roughly ±10 %.

  4. 04

    Cross-range resolution

    Two targets side by side at the same range sit in the beam together until they are more than the beam width apart. At range R that width is Δx = R·θ, with θ in radians. It grows with range. A 1.23° beam is 214.7 m wide at 10 km and 2.1 km wide at 100 km.

  5. 05

    The resolution cell

    ΔR by Δx is the patch the radar cannot split any further, with an area of ΔR·Δx. Range resolution is the same at every distance while cross-range resolution worsens with it, so a distant cell is long across the beam and thin along it.

Formulas

Range resolution
ΔR = c·τ2 = c2B
  • c — speed of light, 299 792 458 m/s
  • τ — pulse width, s (plain pulse: B ≈ 1/τ)
  • B — waveform bandwidth, Hz (pulse compression, FMCW)
Beamwidth from the aperture
θ ≈ 70·λD
  • θ — half-power beamwidth, degrees (≈ 1.22·λ/D rad)
  • λ — wavelength c/f, m
  • D — antenna diameter or width, m
  • 70 — ITU-R F.699 rule, as on the dish gain calculator
Cross-range resolution and cell
Δx = R·θrad, A = ΔR·Δx
  • R — range, m
  • θrad — beamwidth in radians, θ°·π/180
  • A — area of the resolution cell, m²

Worked example

τ = 1 µs, θ = 1.23°, R = 10 km (the defaults)
  1. range resolution ΔR = 299 792 458 · 10−6 / 2 = 149.9 m, bandwidth 1/τ = 1 MHz
  2. beamwidth 1.23° · π/180 = 0.021468 rad
  3. cross-range resolution Δx = 10 000 m · 0.021468 = 214.7 m
  4. resolution cell 149.9 m · 214.7 m = 32 180 m²
  5. aperture mode with its defaults: λ = 299 792 458 / 9.4·109 = 0.031893 m, θ = 70 · 0.031893 / 2.4 = 0.930°

FAQ

Why c·τ/2 and not c·τ?
Because the echo travels out and back. A target ΔR behind another returns its echo 2·ΔR/c later. The two echoes separate once that delay exceeds the pulse length τ, so ΔR = c·τ/2. For 1 µs that is 149.9 m, not 300 m.
How do radars get fine range resolution with long pulses?
With pulse compression. The radar sweeps its frequency (a chirp) or codes its phase inside a long pulse, and the receiver compresses the echo to about 1/B. Resolution then follows the bandwidth, ΔR = c/(2B), not the pulse length. The long pulse carries the energy for range, the bandwidth gives the resolution. An automotive radar with a 4 GHz chirp resolves 3.75 cm.
Why does cross-range resolution get worse with distance?
Because the beam spreads at a fixed angle. Its width grows in proportion to range, so a 1° beam is 175 m wide at 10 km and 1.75 km wide at 100 km. Only a larger antenna, a higher frequency (θ ≈ 70·λ/D) or synthetic-aperture processing (SAR) narrows it.
Why does the aperture mode use 70·λ/D?
Because it is the usual engineering rule for a dish, and the dish gain calculator uses the same one. ITU-R F.699 relates the −3 dB beamwidth to D/λ ≈ 70/θ. The constant depends on how the feed lights the antenna, about 58 for uniform illumination and up to about 72 for a strong taper. For a slotted waveguide or a phased array, type the datasheet beamwidth instead.
Why does my radar’s datasheet quote a coarser range resolution?
Because c·τ/2 is the ideal. A real receiver has limited bandwidth, which stretches the echo, and the display adds its own pixel size. Furuno quotes a range discrimination of 26 m for the FAR-2117, whose shortest pulse of 0.07 µs gives 10.5 m in theory. Treat the formula as the best case.

Resolution tells you what the radar can separate. Whether it sees the area at all depends on the terrain and the earth’s curve. Waveshed maps line of sight from your radar site over real terrain, free in your browser.

Check what your radar site can see →

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