Speed of Sound Calculator
Work out the speed of sound in air, fresh water or seawater, the Mach number of an object, and sound travel time.
What it does
Sound is a pressure wave, and it moves through a medium at the speed that medium allows. NASA Glenn puts it in one line for the ideal gas case: the square of the speed of sound equals gamma times R times T, so the speed depends on the absolute temperature and on the properties of the gas. For dry air that works out at about 331.3 metres per second at 0 °C, rising as the square root of the temperature.
Water is a different story. The NBS paper on the speed of sound in distilled water, hosted by NIST, gives a fitted curve for the whole range from 0 to 100 °C and tabulates the results. At 20 °C the figure is 1,482.7 metres per second, which is why a sound travels more than four times faster in water than in air and why whales carry sound for miles.
Salt matters too. The OpenStax physics text lists seawater at 1,540 metres per second against 1,480 for fresh water at the same temperature, and the exact value moves with salinity, pressure and temperature, so the seawater setting on this page is a reference figure rather than a prediction.
The Mach number is the speed of an object divided by the speed of sound in the medium around it, and it is the measure that decides whether a shock wave forms. Below Mach 1 the waves spread out ahead of the object, at Mach 1 they pile up, and above it they trail behind in a bow wave. NASA defines it the same way.
The tool also gives the travel time, which is the number that matters for ultrasound imaging, for the delay between lightning and thunder, and for any work where a signal is timed against the distance it has to cover.
How to use
- Pick metric or imperial units.
- Choose the medium the sound travels through.
- Enter the temperature of the medium.
- Enter the speed of the object you want the Mach number for.
- Enter the distance the sound has to cover.
- Read the speed of sound, the Mach number and the travel time.
Formula
- c
- Speed of sound in the medium, in metres per second.
- T
- Absolute temperature in kelvin.
- t
- Temperature in degrees Celsius.
- v
- Speed of the object relative to the medium.
- Mach
- Speed of the object divided by the speed of sound.
The 331.3 figure is a rounded normalisation of the ideal gas relation, not an exact constant, so the result matches the usual published values of 331.3 metres per second at 0 °C and 343 metres per second at 20 °C. The air formula assumes dry air: humid air is very slightly faster, because water vapour is lighter than the nitrogen and oxygen it replaces. Seawater is entered as a fixed reference value of 1,540 metres per second because a proper seawater calculation needs salinity and pressure as well as temperature.
Worked example
Example: an object at 340 m/s in air at 20 °C
Defaults: metric units, dry air, 20 °C, an object at 340 m/s and a distance of 10 km.
- Absolute temperature: 20 + 273.15 = 293.15 K.
- Speed of sound: 331.3 x sqrt(293.15 / 273.15) = 343.2 m/s.
- Mach number: 340 / 343.2 = 0.991.
- Travel time over 10 km: 10,000 / 343.2 = 29.14 seconds.
- In feet per second the same speed of sound is 1,126.0 ft/s.
- The tool shows 343.2 m/s, Mach 0.991, 29.14 s and 340.0 m/s.
Reference table
| Medium | Speed | Mach 1 speed in km/h |
|---|---|---|
| Dry air at 0 °C | 331.3 m/s | 1,192.7 km/h |
| Dry air at 10 °C | 337.3 m/s | 1,214.3 km/h |
| Dry air at 20 °C | 343.2 m/s | 1,235.5 km/h |
| Dry air at 30 °C | 349.0 m/s | 1,256.4 km/h |
| Fresh water at 20 °C | 1,482.7 m/s | 5,337.7 km/h |
| Seawater at 20 °C | 1,540.0 m/s | 5,544.0 km/h |
Limits
- Assumes dry air, so a humid day comes out very slightly slow.
- Treats seawater as a fixed reference value, so temperature, salinity and pressure are not modelled.
- Ignores wind, which moves the sound with the air rather than against it.
- Describes a steady medium, so a temperature gradient or a layer of warm air changes the real travel time.
Common mistakes
- Using the speed of sound in air for a calculation in water, which is out by a factor of more than four.
- Entering the temperature in Kelvin when the formula wants Celsius, or the other way round.
- Treating the Mach number as a percentage of the speed of light.
- Forgetting that the travel time is for the sound, not for the object.
- Assuming the speed of sound does not change with the weather, when a cold morning is about 1% slower than a warm afternoon.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is the speed of sound in air at 0 °C?
331.3 x sqrt(273.15 / 273.15) = 331.3 m/s, which is 1,086.9 ft/s.
How fast does sound travel in fresh water at 20 °C?
The fitted curve for distilled water gives 1,482.7 m/s at 20 °C, so it covers a kilometre in 0.67 seconds.
How long does sound take to cross one kilometre of air at 20 °C?
1,000 / 343.2 = 2.91 seconds, which is the gap between the flash of lightning and the thunder that follows.
Questions
How fast does sound travel in air?
About 343 metres per second at 20 °C, which is 1,126 feet per second or about 760 miles per hour. The speed falls as the air cools.
What is a Mach number?
The speed of an object divided by the speed of sound in the air around it. Mach 1 means the object is exactly at the speed of sound, and above Mach 1 it outruns its own pressure waves, which is what makes a shock wave.
Why is sound so much faster in water?
Water is far denser and far less compressible than air, so a pressure disturbance moves through it much faster. The numbers are about 1,483 metres per second in fresh water against 343 in air.
Does humidity matter?
Only a little, and in the direction people do not expect. Humid air is less dense, so sound travels about 0.3% faster in saturated air at 20 °C than in dry air at the same temperature.
Why is there a delay between lightning and thunder?
The light crosses the distance almost instantly while the sound travels at 343 metres per second, so a storm three kilometres away gives about nine seconds between the flash and the bang.
How is this used in medicine?
An ultrasound probe sends a pulse and times the echo. Knowing the speed of sound in tissue lets the machine convert that time into a depth, which is why the assumed speed of sound has to match the tissue being scanned.
Sources
- NASA Glenn Research Center: speed of sound in an ideal gas
- OpenStax University Physics Volume 1: 17.2, speed of sound
- NBS Journal of Research, hosted by NIST: speed of sound in distilled water