The Doppler Effect Calculator

The Doppler effect is the change in observed frequency caused by motion of the source, the observer, or both. Approaching motion raises the pitch, receding motion lowers it, and one formula covers every case.

Source frequencyThe frequency the source emits when nothing is moving, in hertz.Source speedHow fast the source moves, in metres per second.Source directionPositive source speed means the source is closing on the listener.Observer speedHow fast the listener moves, in metres per second.Observer directionPositive observer speed means the listener is closing on the source.Speed of soundAbout 343 metres per second in air at room temperature.

Observed frequency

440

Shift: 0
Shift as a percentage: 0.00%
Wavelength in front of the source: 0.7795
Wavelength behind the source: 0.7795

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

f' = f x (c + vo) / (c - vs)

f': The observed frequency, in hertz
f: The frequency emitted by the source, in hertz
c: The speed of sound, about 343 metres per second in air
vo: Observer speed toward the source, in metres per second
vs: Source speed toward the observer, in metres per second

How to check the result by hand

1
Write down the emitted frequency and the speed of sound
The siren emits 440 hertz and sound travels at 343 metres per second. Both numbers are in SI units, so no conversion is needed.
2
Assign signs to the two speeds
Use positive for motion toward the other party and negative for motion away. With both at rest the observer speed and source speed are zero.
3
Build the numerator and denominator
The numerator is the speed of sound plus the observer speed, which is 343 plus 0. The denominator is the speed of sound minus the source speed, which is 343 minus 0.
4
Divide and compare
440 times 343 divided by 343 is 440 hertz, so no shift appears when nothing moves. Any motion makes the fraction differ from one and the pitch shifts accordingly.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Doppler Effect page.