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Doppler shift calculator

Doppler shift is the change in received frequency caused by relative motion between transmitter and receiver. Closing motion compresses the wave and raises the frequency. Opening motion stretches it and lowers it. The size is Δf = f·(v/c)·cos θ, about 11 kHz on a 435 MHz satellite pass and well under a kilohertz for cars and airliners.

435 MHz is the amateur satellite band.

Default: a low-Earth-orbit satellite, 27 600 km/h. A negative value reverses the motion, so the transmitter recedes where a positive speed closes.

°

0° = coming straight at you, 90° = passing abeam with no shift, 180° = heading straight away.

Doppler shift
+11.1 kHz
plus while closing, minus while opening
While approaching
+11.1 kHz
carrier 435 MHz
While receding
−11.1 kHz
carrier 435 MHz
Fractional shift
+2.56e−5
radial speed +7670 m/s
TXRXf + Δfθ = 0°← stretched behind · f − Δfcompressed ahead · f + Δf →wavefronts · compression exaggeratedv = 27600 km/h →Δf = +11.1 kHzapproaching

The transmitter moves along the green arrow, to the right for a positive speed and to the left for a negative one. Each circle is a wave crest emitted earlier, from a point further back along the motion, so the crests crowd together ahead of it and spread out behind. The receiver sits at angle θ and reads f + Δf where crowded crests arrive, f − Δf where stretched ones do.

Classical approximation, valid for v ≪ c. It assumes a constant velocity and a fixed angle. A real satellite pass changes both continuously, sweeping the shift from + to − within minutes.

How it works

  1. 01

    Motion compresses the wave

    Every wave crest leaves the transmitter from a slightly different place. Closing in, the crests pile up and the arriving wavelength shortens. Moving away, they spread out. The receiver reads that as a carrier sitting above or below its nominal frequency, at unchanged power.

  2. 02

    Take only the radial component

    Only motion along the line between the two stations produces a shift, so multiply by cos θ. At 60° off the line of sight half the shift remains, and abeam at 90° it is exactly zero. Beyond 90° the cosine turns negative, so the range is opening again and the received frequency drops below the carrier. That zero crossing at 90° is the moment a satellite pass flips from approaching to receding.

  3. 03

    Scale the carrier by v/c

    Δf = f · vc · cos θ. The ratio v/c is tiny: 2.6×10−5 at low-Earth-orbit speed, 1.1×10−7 for a car at 120 km/h. The shift is always a small slice of the carrier. It still matters, because it is compared against channel and filter widths, not against the carrier.

  4. 04

    Plan for the swing, not the peak

    A low-Earth-orbit pass sweeps from +Δf at acquisition through zero overhead to −Δf at loss of signal, in ten minutes or less. Narrowband modes such as CW, SSB and GMSK telemetry have to retune continuously, while wideband OFDM links absorb the same shift without noticing it.

Formulas

Classical Doppler shift (v ≪ c)
Δf = f · vc · cos θ
  • Δf — frequency shift, Hz (positive while closing)
  • f — transmitted frequency, Hz
  • v — relative speed, m/s
  • θ — angle between the motion and the line of sight, 0–180°
  • c — speed of light, 299 792 458 m/s
Received frequency
freceived = f + Δf
  • Δf > 0 while closing (θ < 90°)
  • Δf < 0 while receding (θ > 90°)
Exact radial form
freceived = f · 1 + β1 − β , β = v / c
  • differs from the classical result by about β/2
  • needed only when v is a noticeable fraction of c

Worked example

UHF satellite pass (435 MHz, low Earth orbit)
  1. v = 7 660 m/s (low Earth orbit), θ = 0°
  2. Δf = 435×106 · 7 660 / 299 792 458 = 11.1 kHz
  3. received: 435 MHz + 11.1 kHz inbound, 435 MHz − 11.1 kHz outbound
  4. → a 22 kHz swing in one pass, so SSB and CW have to retune continuously

FAQ

When does Doppler shift actually matter?
When the shift becomes comparable to the channel or filter width. A 5.8 GHz link to a car at 120 km/h shifts by about 645 Hz, invisible inside a 20 MHz OFDM channel. The same 645 Hz walks straight out of a 500 Hz CW filter, and a 435 MHz satellite swinging ±11 kHz has to be tracked.
Why does the angle matter so much?
Only the closing speed produces a shift, motion across the line of sight produces none. The shift therefore scales with cos θ: 30° off the line costs 13% of it, 60° off halves it, and at 90°, the closest point of approach where the signal is strongest, the shift is exactly zero. Past 90° the same cosine goes negative and the shift changes sign.
Do I need the relativistic Doppler formula?
Not for anything that flies. The exact radial form differs from f·v/c by roughly β/2, which is 0.0013% at low-Earth-orbit speed and 0.00004% for an airliner. Time dilation adds another (v/c)2/2 on top, some 0.1 Hz at 435 MHz from orbit, far below what any receiver resolves.
Does Doppler break mobile data in a fast car or train?
No. Cellular networks correct for Doppler as a matter of routine. LTE and 5G estimate the frequency offset from reference symbols and retune continuously, and the air interface is specified for several hundred km/h. At 2.6 GHz and 300 km/h the shift is about 720 Hz, a small fraction of a 15 kHz subcarrier. What actually drops the connection on the move is handover between cells, tunnels and cuttings, and fast multipath fading. Doppler does bite where the shift is large or the channel narrow, such as a low-Earth-orbit satellite pass or a narrowband CW or SSB signal.

Tracking a moving station? The path still has to clear the terrain between you. Waveshed draws line-of-sight over real elevation data, free in your browser.

Check the sight line →

Sources & further reading

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