Doppler Effect Calculator
Work out the pitch you actually hear when a sound source or you are moving, then read the wavelength, the size of the shift, and the percent change. Choose the medium or set the air temperature to fix the wave speed, switch speed units between m/s, km/h, mph and ft/s, or flip to light mode for a relativistic redshift or blueshift.
Formula
Worked example
A 440 Hz horn on a car approaching at 30 m/s, listener still, in 20 C air (343 m/s): f′ = 440 × (343 + 0) / (343 − 30) = 440 × 343 / 313 ≈ 482.2 Hz, a 9.6% rise, with an observed wavelength of about 0.711 m.
What the Doppler effect is
The Doppler effect is the change in the observed frequency of a wave when the source, the observer, or both are moving relative to the medium the wave travels through. For sound, that medium is usually air, and the wave travels at roughly 343 metres per second at room temperature. When a source moves toward you, each successive wave crest is emitted from a slightly closer position, so the crests bunch up and arrive more often and you hear a higher pitch. When the source moves away, the crests stretch out and arrive less often, so the pitch drops. The classic example is an ambulance siren: it sounds high as it approaches, then suddenly lower the instant it passes and begins to recede. This calculator reports the observed frequency, the size of the shift in hertz and as a percent, and the observed wavelength.
The formula and its sign convention
The observed frequency is f′ = f · (v ± v_o) / (v ∓ v_s), where v is the wave speed, v_o is the observer speed, and v_s is the source speed. The signs encode the direction of motion. In the numerator you add the observer speed when the observer moves toward the source and subtract it when moving away. In the denominator you subtract the source speed when the source moves toward the observer and add it when moving away. The upper signs (add on top, subtract on bottom) both push the frequency up, which matches the intuition that any approach raises the pitch. This calculator handles the signs through the two direction selectors, so you only enter positive speeds, in whichever unit is handy: m/s, km/h, mph or ft/s.
Wave speed: medium and temperature
The shift scales with the wave speed, so getting that speed right matters. In air the speed of sound is not fixed: it rises with temperature, from about 331 m/s at 0 C to roughly 343 m/s at 20 C and 349 m/s at 30 C, following 331.3 × √(1 + T/273.15). Set the air temperature and the calculator updates the wave speed automatically. Sound also travels far faster in denser media: about 1481 m/s in fresh water, 1500 m/s in sea water and nearly 6000 m/s in steel, all selectable here. If you have a more precise figure, for example one that accounts for humidity and air pressure, choose the custom option and type it in.
Why source and observer are not symmetric
It is tempting to assume that a source moving toward a still observer at 30 m/s gives the same result as an observer moving toward a still source at 30 m/s, but the equation shows they differ. Moving the observer changes the numerator linearly, while moving the source changes the denominator, which has a stronger, non-linear effect as the source speed approaches the wave speed. This asymmetry exists because the medium provides a fixed reference frame for sound. As the source speed nears the wave speed the denominator approaches zero and the predicted frequency rises without bound; at exactly that speed (Mach 1) the source keeps pace with its own wavefronts, producing the shock wave we hear as a sonic boom. The Mach-number output flags when you cross that threshold.
Light mode and the relativistic Doppler effect
Light needs no medium, so its Doppler shift depends only on the relative speed between source and observer and must respect special relativity. Switch to light mode and the calculator uses f′ = f × √((1 + β)/(1 − β)) for approach and the inverse for recession, where β is the closing speed divided by the speed of light. Approaching light is blueshifted to a higher frequency and shorter wavelength; receding light is redshifted. This is the redshift astronomers measure to find how fast distant galaxies recede and to trace the expansion of the universe, and it is the principle behind Doppler radar and police speed guns.
Approaching vs receding pitch (440 Hz source, still listener, 343 m/s air)
| Source speed (m/s) | Approaching (Hz) | Receding (Hz) |
|---|---|---|
| 10 | 453.2 | 427.5 |
| 30 | 482.2 | 404.6 |
| 50 | 515.1 | 384 |
| 100 | 621.1 | 340.7 |
Observed frequency for a source moving directly toward or away from a still observer.
Frequently asked questions
What is the formula for the Doppler effect with sound?
The observed frequency is f′ = f · (v ± v_o) / (v ∓ v_s), where v is the wave speed (about 343 m/s in air at 20 C), v_o is the observer speed, and v_s is the source speed. Use the upper signs (+ on top, − on bottom) for motion that closes the gap, which raises the pitch.
How does temperature change the result?
The speed of sound in air rises with temperature, about 0.6 m/s per degree Celsius, following 331.3 × √(1 + T/273.15). Warmer air carries sound faster, which slightly raises the Doppler-shifted frequency for the same speeds. Set the air temperature and the calculator updates the wave speed for you.
Why does a siren drop in pitch as it passes?
While the siren approaches, its motion compresses the sound waves and you hear a higher frequency. The moment it passes and starts receding, the waves stretch out, so the frequency you hear drops. The change is abrupt because the direction of the source motion relative to you reverses as it goes by.
How is the Doppler effect for light different?
Light needs no medium, so only the relative speed between source and observer matters, and the formula is relativistic: f′ = f × √((1 + β)/(1 − β)) for approach, where β is the closing speed over the speed of light. Approaching light blueshifts to higher frequency; receding light redshifts, which is how astronomers measure the expansion of the universe.
Does the distance to the source affect the Doppler shift?
No. The shift depends only on the speeds of the source and observer relative to the medium (or, for light, their relative speed), not on how far apart they are. Distance affects loudness, but a source approaching at a given speed produces the same frequency shift whether it is near or far.