Doppler Frequency Shift

Δf = fc × v / c

Quick answer

This calculator solves Δf = f_c × v / c for Doppler Shift. With Carrier Frequency 2.4 GHz, Relative Velocity 0.5, the result is 4.003 Hz. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Doppler Shift (Hz)
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Formula

Δf = f_c × v / c

Description

The Doppler effect shifts the frequency of electromagnetic waves when there is relative motion between transmitter and receiver. The frequency increases when approaching (positive shift) and decreases when receding (negative shift). This simplified formula is valid for velocities much less than the speed of light (v << c), which covers all terrestrial applications. Doppler shift is the fundamental principle behind police radar guns, weather radar, automotive radar (ACC, collision avoidance), medical ultrasound velocity measurement, and satellite communication frequency planning.

Variables

  • Δf — Doppler frequency shift (Hz)
  • f_c — Carrier (transmitted) frequency (Hz)
  • v — Relative velocity between source and observer (m/s)

Practical Notes

c = 299,792,458 m/s. At 24 GHz (automotive radar), a car at 100 km/h (27.8 m/s) produces Δf = 24e9 × 27.8/3e8 = 2222 Hz. At 77 GHz: Δf = 7122 Hz. For radar, the round-trip doubles the Doppler shift: Δf_radar = 2 × fc × v/c. GPS satellite Doppler shifts are ±5 kHz due to satellite orbital velocity of ±800 m/s relative to the receiver.

Symbols and units

Symbol Meaning Default unit Accepted units
df Doppler Shift Hz Hz, kHz, MHz, GHz
fc Carrier Frequency GHz Hz, kHz, MHz, GHz
v Relative Velocity — —

Step by step

  1. 1. What you know: Carrier Frequency 2.4 GHz, Relative Velocity 0.5
  2. 2. The relation: Δf = f_c × v / c
  3. 3. Substitute: fc = 2.4 GHz, v = 0.5
  4. 4. Result: Doppler Shift = 4.003 Hz

Worked examples

Minimum range

Given: Carrier Frequency 100 MHz, Relative Velocity 0.025

Result: Doppler Shift = 0.008339 Hz

Low range

Given: Carrier Frequency 1 GHz, Relative Velocity 0.25

Result: Doppler Shift = 0.8339 Hz

Typical

Given: Carrier Frequency 2.4 GHz, Relative Velocity 0.5

Result: Doppler Shift = 4.003 Hz

High range

Given: Carrier Frequency 10 GHz, Relative Velocity 0.8

Result: Doppler Shift = 26.69 Hz

Maximum range

Given: Carrier Frequency 100 GHz, Relative Velocity 8

Result: Doppler Shift = 2.669 kHz

Solving for each variable

Solve for Doppler Shift

Carrier Frequency 100 MHz, Relative Velocity 0.025 → 0.008339 Hz

Solve for Carrier Frequency

Doppler Shift 5 Hz, Relative Velocity 0.025 → 59.96 GHz

Solve for Relative Velocity

Doppler Shift 5 Hz, Carrier Frequency 100 MHz → 14.99

How Doppler Shift changes with Carrier Frequency

Carrier Frequency (input) Doppler Shift (result)
0.24 GHz 0.4003 Hz
0.6 GHz 1.001 Hz
1.2 GHz 2.001 Hz
1.8 GHz 3.002 Hz
2.4 GHz 4.003 Hz
3.6 GHz 6.004 Hz
4.8 GHz 8.006 Hz
9.6 GHz 16.01 Hz
16.8 GHz 28.02 Hz
24 GHz 40.03 Hz

The same result in other units

Unit Value
Hz 4.003
kHz 0.004003

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Frequently asked questions

How do you calculate Doppler Frequency Shift?

Use Δf = f_c × v / c. With Carrier Frequency 2.4 GHz, Relative Velocity 0.5, Doppler Shift works out to 4.003 Hz.

What is the formula for Doppler Frequency Shift?

The formula is Δf = f_c × v / c. The Doppler effect shifts the frequency of electromagnetic waves when there is relative motion between transmitter and receiver.

How do you find Carrier Frequency when you know the other values?

Rearrange for Carrier Frequency: with Doppler Shift 5 Hz, Relative Velocity 0.025, Carrier Frequency is 59.96 GHz.

How do you find Relative Velocity when you know the other values?

Rearrange for Relative Velocity: with Doppler Shift 5 Hz, Carrier Frequency 100 MHz, Relative Velocity is 14.99.

What units does Doppler Frequency Shift use?

Doppler Shift is shown in Hz, kHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Signal & RF formulas →
Wavelength Free Space Path Loss Signal-to-Noise Ratio Nyquist Sampling Rate Link Budget Antenna Gain Skin Depth Friis Noise Figure (3-stage)

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