Doppler Effect Calculator
Enter a source frequency, the speed of sound, how fast the source moves, and whether it is approaching or receding to get the observed frequency — and see why a passing siren rises then drops in pitch.
Approaching or receding
Enter the source frequency, the speed of sound, the source speed, and the direction of travel, and the calculator returns the observed frequency in hertz.
Use SI units
Frequency in hertz and speeds in metres per second give the result in hertz — divide km/h by 3.6 to get m/s before you start.
What is the Doppler effect?
Why an approaching pitch sounds higher
The Doppler effect is the change in the frequency a stationary observer hears when the sound source moves relative to them. This Doppler effect calculator handles a source moving straight toward or away from you. As it approaches, each successive wave is emitted a little closer than the last, so the waves bunch up and arrive more often — the pitch you hear rises above the frequency the source actually emits. As it recedes, the waves stretch out and the pitch drops below it. It is the reason a passing siren or race car rises then drops in pitch the instant it goes by.
Enter a source frequency, the speed of sound, the source speed, and the direction of travel to get the observed frequency instantly.
For a source moving toward a stationary observer, the observed frequency is the source frequency multiplied by the speed of sound divided by the speed of sound minus the source speed; for a source moving away, the source speed is added instead.
f′ = f × v ÷ (v ∓ vₛ)Here f is the source frequency, v the speed of sound (about 343 m/s in air at 20 °C), and vₛ the speed of the source. Subtract vₛ from v when the source approaches — a faster approach shrinks the denominator and pushes the observed frequency higher; add vₛ to v when it recedes, which enlarges the denominator and lowers the pitch.
Suppose a horn sounding 440 Hz approaches you at 30 m/s, with sound travelling at 343 m/s.
Find the closing denominator
343 − 30 = 313 — the speed of sound minus the source speed.
Divide the speed of sound by it
343 ÷ 313 = 1.0958 — the factor by which the pitch rises.
Multiply by the source frequency
440 × 1.0958 = 482.17 Hz — the observed frequency, noticeably higher than the 440 Hz emitted, so the pitch rises.
The formula is exact for this case, but a few practical points are worth keeping in mind.
Moving source, stationary observer
This calculator assumes a stationary observer and a source moving directly toward or away along the line between you — pick the direction and it uses (v − vₛ) for an approaching source or (v + vₛ) for a receding one. The approaching formula is undefined once the source reaches the speed of sound (v − vₛ ≤ 0), where a shock wave forms, so the calculator returns no result there. Keep your units consistent — hertz and metres per second — and convert km/h to m/s by dividing by 3.6.