Doppler Effect Calculator
Doppler shift for sound and light, with redshift z.
About this tool
For sound, enter the frequency, the speed of sound and how fast the source and observer move towards each other. You get the frequency approaching and moving apart and the pitch change in semitones. For light, enter a wavelength and recession speed to get the redshift.
How the Doppler effect works
When a source of waves moves towards you, each wave starts a little closer, so they arrive bunched up: a higher frequency. Moving away stretches them out. For sound in still air, f' = f ร (c + v_observer) รท (c โ v_source), with speeds positive when the two are closing. A 700 Hz siren approaching at 30 m/s (108 km/h) sounds like 767 Hz, then drops to 644 Hz as it recedes, a fall of about three semitones that you hear as it passes. If the source moves at the speed of sound, waves pile into a shock front: the sonic boom. Light has no medium, so it uses the relativistic formula, observed wavelength = emitted ร โ((1 + ฮฒ) รท (1 โ ฮฒ)), where ฮฒ is the recession speed as a fraction of c. A galaxy moving away at 10% of light speed shows a redshift z of 0.106. Doppler shifts also underpin weather radar, police speed guns and ultrasound blood-flow scans. Honest limits: the formulas assume motion along the line of sight and no wind; very distant galaxies' redshift comes from the expansion of space. The speed of sound calculator and the time dilation calculator are related.
Frequently asked questions
What is the Doppler effect?
The change in frequency of a wave when the source and observer move relative to each other.
Why does a siren's pitch drop as it passes?
Approaching, the sound waves are compressed (higher pitch); moving away, they're stretched (lower pitch).
What is redshift?
The stretching of light from a receding source to longer, redder wavelengths, measured as z = (observed โ emitted) รท emitted.
What is the Doppler formula for sound?
f' = f ร (c + vo) รท (c โ vs), with speeds positive when the source and observer approach each other.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.