Quick answer
The Doppler formula f′ = f × (c + vₒ) ÷ (c − vₛ) gives the observed frequency. A 440 Hz source moving toward a still observer at 20 m/s with sound at 343 m/s is heard at 467.245 Hz, a shift of 27.245 Hz.
Enter the source frequency, source speed, observer speed and wave speed. The calculator returns the observed frequency and shift. Use this doppler effect calculator to check your own figures.
Related tools: Sound Level Calculator: Combine decibel levels, or convert sound intensity to decibels. Effect Size (Cohen's d) Calculator: Cohen's d for two groups. Dew Point Calculator: Dew point from temperature and relative humidity.
How to use the Doppler Effect Calculator
- Enter source frequency (Hz) (above 0).
- Enter source speed toward the observer (m/s).
- Enter observer speed toward the source (m/s).
- Enter wave speed (m/s) (above 0). It starts at 343.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Source frequency | A number, in Hz | > 0 |
| Source speed toward the observer | A number, in m/s | — |
| Observer speed toward the source | A number, in m/s | — |
| Wave speed | A number, in m/s | > 0, starts at 343 |
Formula and method
Formula
f′ = f × (c + v_o) ÷ (c − v_s)
IEEE-754 double precision; shown to the decimals indicated.
Default wave speed 343 m/s is sound in air at about 20 °C; use a negative speed for movement away.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Source frequency = 440; Source speed toward the observer = 20; Observer speed toward the source = 0; Wave speed = 343.
| Result | Value |
|---|---|
| Observed frequency | 467.245 Hz |
| Shift | 27.245 Hz |
Example 2
Inputs: Source frequency = 1000; Source speed toward the observer = 0; Observer speed toward the source = 15; Wave speed = 343.
| Result | Value |
|---|---|
| Observed frequency | 1,043.732 Hz |
| Shift | 43.732 Hz |
Example 3
Inputs: Source frequency = 500; Source speed toward the observer = -30; Observer speed toward the source = 10; Wave speed = 343.
| Result | Value |
|---|---|
| Observed frequency | 473.19 Hz |
| Shift | -26.81 Hz |
The first line is the headline result (observed frequency). Below it the doppler Effect Calculator lists shift, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
f′ = 440 × 343 ÷ (343 − 20) = 440 × 1.0619 = 467.2 Hz. As the source passes and recedes, the denominator becomes 363, giving 415.7 Hz, the familiar drop in pitch of a passing siren.
Where this estimate stops applying
The source speed must be below the wave speed. The formula is for sound in a still medium; light needs a relativistic version. Speeds toward each other are positive.
How the result changes with source frequency
Holding every other input at the first worked example, this table changes only source frequency. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Source frequency | Observed frequency | Shift |
|---|---|---|
| 220 | 233.622 Hz | 13.622 Hz |
| 440 | 467.245 Hz | 27.245 Hz |
| 880 | 934.489 Hz | 54.489 Hz |
| 1760 | 1,868.978 Hz | 108.978 Hz |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Source speed toward the observer: entering "400" shows "The source speed must be below the wave speed." beside that field and no result.
- Source frequency: entering "0" shows "Source frequency must be greater than 0." beside that field and no result.
Choosing between the Doppler Effect Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Sound Level Calculator](/science/sound-level-calculator/) | use | Combined level |
| [Effect Size (Cohen's d) Calculator](/statistics/effect-size-calculator/) | mean 1, sD 1 and n₁ | Cohen's d |
| [Dew Point Calculator](/science/dew-point/) | air temperature and relative humidity | Dew point |
| [Acceleration Calculator](/science/acceleration-calculator/) | initial velocity, final velocity and time | Acceleration |
| [Mole Calculator](/science/mole/) | start from and molar mass | Amount |
Background: environment and acoustics
Decibels are a logarithmic scale, so sound levels cannot be added arithmetically: two equal sources raise the level by about 3 dB, not double it. Environmental and emissions results depend on the factors behind them (for example the US EPA's equivalency factors), which are averages for a country, fuel and year.
Use the result to compare scenarios rather than as a measured value.
Assumptions and limitations
- Source speed must be below the wave speed
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for source speed toward the observer and source frequency to confirm this.
Frequently asked questions
Why does a siren change pitch?
The wave crests bunch up approaching and spread out receding.
What is the speed of sound in air?
About 343 m/s at 20 °C.
Does it work for light?
Use the relativistic formula.
What does the Doppler Effect Calculator calculate?
Observed frequency from source and observer speeds. It returns Observed frequency and Shift.
What formula does the Doppler Effect Calculator use?
f′ = f × (c + v_o) ÷ (c − v_s). Default wave speed 343 m/s is sound in air at about 20 °C; use a negative speed for movement away.
What do I need to enter in the doppler Effect Calculator?
You enter Source frequency (Hz), Source speed toward the observer (m/s), Observer speed toward the source (m/s) and Wave speed (m/s).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Source speed must be below the wave speed.
What is an example of a doppler Effect result?
With source frequency 440, source speed toward the observer 20, observer speed toward the source 0 and wave speed 343, the observed frequency is 467.245 Hz.
Related calculators
- Sound Level Calculator — Combine decibel levels, or convert sound intensity to decibels.
- Effect Size (Cohen's d) Calculator — Cohen's d for two groups.
- Dew Point Calculator — Dew point from temperature and relative humidity.
- Acceleration Calculator — Average acceleration from change in velocity over time.
- Mole Calculator — Convert between mass, moles and number of particles.
- Density Calculator — Solve mass, density or volume.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.