About this calculator
An ambulance siren sounds higher as it approaches and lower as it moves away. That is the Doppler effect: motion squashes or stretches the sound waves reaching you.
Enter the sound's original frequency and the speed of the source and observer. Speeds are positive when moving towards the other and negative when moving away. The speed of sound is about 343 m/s in air at 20 °C.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
440 Hz source approaching at 30 m/s
- Frequency heard
- 482.172524 Hz
- Shift
- +42.172524 Hz
- Shift as a percentage
- 9.584665%
- Pitch
- Higher than the original
A 440 Hz sound is heard as 482.172524 Hz when the source moves at 30 m/s and the observer at 0 m/s (positive means moving towards the other).
Show the working
- Doppler effect for sound: f′ = f × (c + v_observer) ÷ (c − v_source). Speeds are positive when moving towards each other.
- f′ = 440 × (343 + 0) ÷ (343 − 30) = 482.172524 Hz.
- Use negative speeds for a source or observer moving away. The effect for light and radio waves needs a different (relativistic) formula.
Same source moving away
- Frequency heard
- 404.61126 Hz
- Shift
- -35.38874 Hz
- Shift as a percentage
- -8.042895%
- Pitch
- Lower than the original
A 440 Hz sound is heard as 404.61126 Hz when the source moves at -30 m/s and the observer at 0 m/s (positive means moving towards the other).
Show the working
- Doppler effect for sound: f′ = f × (c + v_observer) ÷ (c − v_source). Speeds are positive when moving towards each other.
- f′ = 440 × (343 + 0) ÷ (343 − -30) = 404.61126 Hz.
- Use negative speeds for a source or observer moving away. The effect for light and radio waves needs a different (relativistic) formula.
You run at 5 m/s towards a 1,000 Hz speaker
- Frequency heard
- 1,014.577259 Hz
- Shift
- +14.577259 Hz
- Shift as a percentage
- 1.457726%
- Pitch
- Higher than the original
A 1,000 Hz sound is heard as 1,014.577259 Hz when the source moves at 0 m/s and the observer at 5 m/s (positive means moving towards the other).
Show the working
- Doppler effect for sound: f′ = f × (c + v_observer) ÷ (c − v_source). Speeds are positive when moving towards each other.
- f′ = 1,000 × (343 + 5) ÷ (343 − 0) = 1,014.577259 Hz.
- Use negative speeds for a source or observer moving away. The effect for light and radio waves needs a different (relativistic) formula.
The formula
f′ = f × (c + vobserver) ÷ (c − vsource), where c is the speed of sound. Both speeds count as positive when the source and observer are moving towards each other.
Speed of sound
- Air at 0 °C: about 331 m/s
- Air at 20 °C: about 343 m/s
- Water: about 1,480 m/s
- Steel: about 5,960 m/s
In air it rises by roughly 0.6 m/s for each degree Celsius.
Where it applies
Sirens, passing cars and trains, bats and radar speed guns use the Doppler effect. The formula here is for sound, which needs a medium. For light and radio waves, relativity changes the formula, so use a relativistic Doppler calculator at high speeds.
Frequently asked questions
Why does the pitch change?
A moving source crowds the waves ahead of it, raising the frequency, and stretches them behind, lowering it.
What if the source moves faster than sound?
Then it outruns its own sound and creates a shock wave (a sonic boom). The simple formula doesn't apply.
Does the loudness change too?
Yes, but that depends on distance, not on the Doppler effect.
Which speed is positive?
Movement towards the other party is positive; away is negative.
Does it work for light?
Not with this formula. Light needs the relativistic Doppler effect.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.