Why does this page show ±λ·PRF/4 when my textbook says λ·PRF/2?

Both are right, they count differently. This page uses the coherent (I/Q) convention. The radar measures the sign of the Doppler shift, which is unambiguous over ±PRF/2, so speeds from −λ·PRF/4 to +λ·PRF/4 read correctly: ±24.98 m/s at 1 kHz and 3 GHz. Books that quote λ·PRF/2 = 49.97 m/s mean the full span from −v to +v, a magnitude-only radar that cannot tell approaching from receding, or the first blind speed. Weather radar calls the ± value the Nyquist velocity.

Why can’t a radar have both a long unambiguous range and a high unambiguous velocity?

Because both depend on the PRF in opposite directions, and their product is fixed: Runamb·vunamb = c·λ/8, about 4.0·10^6 m²/s at 2.8 GHz. Switch between the two NEXRAD presets to see it. At 318 Hz the radar measures 471 km but only ±8.5 m/s, at 1300 Hz ±34.8 m/s but only 115 km. That is why NEXRAD runs a low-PRF surveillance scan and a high-PRF Doppler scan, and why radars are grouped into low, medium and high PRF.

What is a blind speed?

A radial speed at which a moving-target (MTI) radar cannot see a target. If the target moves exactly n half-wavelengths per pulse interval, its echo has the same phase on every pulse, and the clutter filter removes it like a building. The blind speeds are n·λ·PRF/2: 49.97, 99.93 and 149.9 m/s at the defaults. Staggered or switched PRFs push the first shared blind speed far higher.

Why can’t a radar see targets right next to it?

Because its receiver is switched off while it transmits. A monostatic radar sends and receives through one antenna, so echoes that arrive during the pulse are lost. The blind range is c·τ/2, 150 m per microsecond of pulse. Furuno quotes a minimum range of 22 m for the FAR-2117, whose shortest pulse of 0.07 µs alone gives 10.5 m. A real receiver also needs a moment to recover after each pulse.

Does pulse compression change the PRF trade-off?

No. Pulse compression changes what a single pulse delivers. Range resolution becomes c/(2B), and the matched filter adds the time-bandwidth product B·τ as gain, 20 dB for 10 µs and 10 MHz. Unambiguous range c/(2·PRF) and velocity ±λ·PRF/4 depend only on the PRF and the wavelength, so they stay where they were. The long transmitted pulse does widen the blind range c·τ/2, which radars cover with a short fill pulse.

Peak power or average power: which one matters?

Both, for different things. Peak power sets what a single pulse can detect, and the radar range equation uses it for one pulse. Average power sets the electricity bill, the heating and the RF exposure. Over many pulses, detection depends on the energy collected, average power times dwell time. A 1 MW, 1 µs, 1 kHz radar averages only 1 kW. This duty cycle is not LoRa’s 1 % duty cycle, which is a legal limit on transmit time per hour.

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PRF calculator: unambiguous range, blind speeds and duty cycle

The pulse repetition frequency (PRF) sets how far a pulsed radar can measure without ambiguity, c/(2·PRF), and how fast a target may move before its Doppler shift folds over, ±λ·PRF/4. This calculator gives both, plus the blind speeds, the blind range close to the radar, the duty cycle, average power and energy per pulse.

Preset

A selection, read 7 November 2026. NEXRAD values from its Wikipedia article (318–1300 Hz, 1.57–4.57 µs, 750 kW), paired here for illustration. The marine pulse is Furuno FAR-2117’s 0.07 µs at 3000 Hz, 12 kW. The airborne preset is illustrative and keeps your peak power.

PRF (or PRI)

Pulses per second. Pick a “PRI” unit to type the time between pulses instead.

Carrier frequency

Sets the wavelength, so it changes the velocities. The range values do not depend on it.

Pulse width τ

Length of one transmitted pulse. It sets the blind range and the duty cycle.

Peak power

Power during the pulse. It changes only average power and energy, nothing about range or speed.

Pulses per dwell N (optional)

Pulses processed together in one Doppler measurement. Leave 0 for none. With N set, the velocity resolution and the energy per dwell appear.

Max. unambiguous range

149.9

echoes from farther away fold back as close ghosts

Max. unambiguous velocity

±24.98

full span from −v to +v: 49.97 m/s

First blind speed

49.97

next: 99.93 m/s and 149.9 m/s

Blind range

149.9

the receiver is off while the pulse is sent

Duty cycle

0.1 %

ratio 0.001 · −30.0 dB

Average power

peak power × duty cycle

Energy per pulse

peak power × pulse width

PRI (pulse interval)

1 / PRF

Velocity follows the coherent (I/Q) convention. The Doppler shift is unambiguous between −PRF/2 and +PRF/2, so speeds up to 24.98 m/s read correctly. Books that give λ·PRF/2 = 49.97 m/s as the maximum unambiguous velocity mean the full span from −v to +v, a radar that cannot tell approaching from receding, or the first blind speed. The physics is the same.
At λ = 9.993 cm, range times velocity is fixed: R_unamb × v_unamb = c·λ/8 = 3.745·10⁶ m²/s, whatever the PRF. Ten times the range leaves a tenth of the velocity.

Log–log axes. The green line holds every pair of maximum unambiguous range and velocity that a radar on this carrier frequency can have. Their product is fixed at c·λ/8, so the line has slope −1. The large dot is your PRF, with dashed lines to both axes. The small dots on the line mark each tenfold step of PRF from 10 Hz (lower right) to 1 MHz (upper left). A higher carrier frequency moves the line down. The amber hatched strip on the left is the blind range c·τ/2, visible once the pulse is longer than 1 µs. Peak power and the number of pulses do not change this drawing. Range and velocity use the units you picked last.

A monostatic pulsed radar with one constant PRF. Velocities are radial, along the line of sight. Staggered or multiple PRFs, which radars use to resolve the ambiguities, are not modelled. The blind range counts the pulse alone, without receiver recovery time. Furuno is a trademark of Furuno Electric Co., Ltd. Waveshed is not affiliated with it.

How it works

01
Range from PRF

An echo must come back before the next pulse leaves, or the radar cannot tell which pulse it belongs to. In one pulse interval (PRI) the pulse travels out and back over c/(2·PRF), 149.9 km at 1 kHz. A target farther away shows up as a ghost at a short range.
02
Velocity from PRF and wavelength

A pulse-Doppler radar samples the phase of each echo once per pulse. Sampled at the PRF, the Doppler shift f_d = 2v/λ is unambiguous between −PRF/2 and +PRF/2, so radial speeds up to ±λ·PRF/4 read correctly. Faster targets fold over to a wrong speed.
03
Blind speeds

A target that moves a whole number of half-wavelengths between two pulses returns the same phase every time. A moving-target filter (MTI) takes it for a fixed echo and removes it. The blind speeds are v_n = n·λ·PRF/2, twice the unambiguous velocity and its multiples. Staggered PRFs move them apart.
04
Blind range and duty cycle

The receiver is off while the transmitter sends, so echoes from closer than c·τ/2 are lost, 150 m per microsecond of pulse. The share of time on air is the duty cycle D = τ·PRF. Average power is peak power times D, and the blind range is exactly the share D of the unambiguous range.
05
Choose the PRF

Range and velocity pull the PRF in opposite directions, and their product c·λ/8 is fixed by the frequency. Low PRF suits long-range surveillance, high PRF suits fast targets. NEXRAD alternates between both. If the radar processes N pulses together, its velocity resolution is λ·PRF/(2N).
06
Pulse compression

Modern radars rarely send a plain short pulse. Pulse compression modulates a long pulse with a linear FM chirp or a phase code, and a matched filter in the receiver squeezes the echo back into a short spike. Range resolution then follows the bandwidth, c/(2B), instead of the pulse length. The long pulse carries more energy and average power, so the radar reaches farther without coarser range cells. The compression gain is the time-bandwidth product B·τ. A 10 µs pulse with 10 MHz of bandwidth gives 100, or 20 dB, with 15 m cells instead of 1.5 km. The blind range still grows with the transmitted pulse, c·τ/2, 1.5 km here, so radars cover it with a short fill pulse or interleaved short pulses. Compression leaves the PRF trade-off unchanged. Unambiguous range and velocity still depend only on the PRF and the wavelength.

Formulas

Maximum unambiguous range and velocity

R_unamb = c2·PRF, v_unamb = ±λ·PRF4

c — speed of light, 299 792 458 m/s
PRF — pulse repetition frequency, Hz (PRI = 1/PRF)
λ — wavelength c/f, m
± — coherent (I/Q) Doppler, unambiguous over ±PRF/2; full span λ·PRF/2

Blind speeds and blind range

v_n = n·λ·PRF2, R_blind = c·τ2

n — 1, 2, 3 …
τ — pulse width, s
R_blind — receiver off while transmitting (monostatic radar)

Duty cycle, average power, energy per pulse

D = τ·PRF, P_avg = P_peak·D

P_peak — peak power, W
E = P_peak·τ — energy per pulse, J

The trade-off

R_unamb·v_unamb = c·λ8

independent of PRF
Δv = λ·PRF/(2N) — velocity resolution of an N-pulse dwell

Worked example

1 kHz PRF, 3 GHz, 1 µs pulse, 1 MW peak (the defaults)

wavelength λ = 299 792 458 / 3·10⁹ = 0.09993 m, pulse interval 1/1000 = 1 ms
unambiguous range 299 792 458 / (2 · 1000) = 149 896 m = 149.9 km
unambiguous velocity 0.09993 · 1000 / 4 = ±24.98 m/s, full span 49.97 m/s. Check: 149 896 · 24.98 = 3.745·10⁶ m²/s = c·λ/8
blind speeds n · 0.09993 · 1000 / 2 = 49.97, 99.93 and 149.9 m/s
blind range 299 792 458 · 10⁻⁶ / 2 = 149.9 m
duty cycle 10⁻⁶ · 1000 = 0.001 = 0.1 % (−30.0 dB), average power 10⁶ W · 0.001 = 1 kW, energy per pulse 10⁶ W · 10⁻⁶ s = 1 J

FAQ

Why does this page show ±λ·PRF/4 when my textbook says λ·PRF/2?: Both are right, they count differently. This page uses the coherent (I/Q) convention. The radar measures the sign of the Doppler shift, which is unambiguous over ±PRF/2, so speeds from −λ·PRF/4 to +λ·PRF/4 read correctly: ±24.98 m/s at 1 kHz and 3 GHz. Books that quote λ·PRF/2 = 49.97 m/s mean the full span from −v to +v, a magnitude-only radar that cannot tell approaching from receding, or the first blind speed. Weather radar calls the ± value the Nyquist velocity.
Why can’t a radar have both a long unambiguous range and a high unambiguous velocity?: Because both depend on the PRF in opposite directions, and their product is fixed: R_unamb·v_unamb = c·λ/8, about 4.0·10⁶ m²/s at 2.8 GHz. Switch between the two NEXRAD presets to see it. At 318 Hz the radar measures 471 km but only ±8.5 m/s, at 1300 Hz ±34.8 m/s but only 115 km. That is why NEXRAD runs a low-PRF surveillance scan and a high-PRF Doppler scan, and why radars are grouped into low, medium and high PRF.
What is a blind speed?: A radial speed at which a moving-target (MTI) radar cannot see a target. If the target moves exactly n half-wavelengths per pulse interval, its echo has the same phase on every pulse, and the clutter filter removes it like a building. The blind speeds are n·λ·PRF/2: 49.97, 99.93 and 149.9 m/s at the defaults. Staggered or switched PRFs push the first shared blind speed far higher.
Why can’t a radar see targets right next to it?: Because its receiver is switched off while it transmits. A monostatic radar sends and receives through one antenna, so echoes that arrive during the pulse are lost. The blind range is c·τ/2, 150 m per microsecond of pulse. Furuno quotes a minimum range of 22 m for the FAR-2117, whose shortest pulse of 0.07 µs alone gives 10.5 m. A real receiver also needs a moment to recover after each pulse.
Does pulse compression change the PRF trade-off?: No. Pulse compression changes what a single pulse delivers. Range resolution becomes c/(2B), and the matched filter adds the time-bandwidth product B·τ as gain, 20 dB for 10 µs and 10 MHz. Unambiguous range c/(2·PRF) and velocity ±λ·PRF/4 depend only on the PRF and the wavelength, so they stay where they were. The long transmitted pulse does widen the blind range c·τ/2, which radars cover with a short fill pulse.
Peak power or average power: which one matters?: Both, for different things. Peak power sets what a single pulse can detect, and the radar range equation uses it for one pulse. Average power sets the electricity bill, the heating and the RF exposure. Over many pulses, detection depends on the energy collected, average power times dwell time. A 1 MW, 1 µs, 1 kHz radar averages only 1 kW. This duty cycle is not LoRa’s 1 % duty cycle, which is a legal limit on transmit time per hour.

PRF tells you how far the radar can measure. Whether it sees a low target at that range depends on the terrain in between. Waveshed draws line of sight from your radar site over real terrain, free in your browser.

Map what your radar site can see →

Related guides

LOS vs RF (FSPL & ITM) — line of sight decides whether a low target is visible at all
Plan radio coverage (RF / ITM) — from a site and an antenna height to a coverage map

Sources & further reading

M. I. Skolnik, Introduction to Radar Systems, 3rd ed., McGraw-Hill, 2001 ↗ — ch. 1 for unambiguous range, duty cycle and peak versus average power, ch. 3 for MTI, blind speeds and staggered PRFs. Google Books record, because the publisher’s page only redirects to a search
M. A. Richards, Fundamentals of Radar Signal Processing, 2nd ed., McGraw-Hill, 2014 ↗ — Doppler sampled at the PRF, range and velocity ambiguity, low, medium and high PRF
IEEE 686-2024 — IEEE Standard for Radar Definitions ↗ — the reference vocabulary for radar terms. Paywalled and not read for this tool
Furuno FAR-2117/2127 series specifications (NOAA PSL mirror) ↗ — the 0.07 µs pulse at 3000 Hz, 12 kW, 9410 MHz and the 22 m minimum range
NEXRAD — Wikipedia ↗ — PRF 318–1300 Hz, pulse 1.57–4.57 µs, 750 kW, 2.7–3.0 GHz, read 7 November 2026
Radar signal characteristics — Wikipedia ↗ — unambiguous range and velocity, read 7 November 2026

PRF calculator: unambiguous range, blind speeds and duty cycle

How it works

Range from PRF

Velocity from PRF and wavelength

Blind speeds

Blind range and duty cycle

Choose the PRF

Pulse compression

Formulas

Worked example

FAQ

Related guides

Sources & further reading

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