Speed Of Sound Calculator

What the speed of sound calculator does

Sound travels through air at a speed that depends on the air's temperature. This calculator finds the speed of sound in air from the temperature you enter, and includes a quick reference of tabulated speeds at common temperatures.

Below is what the speed of sound is, why temperature governs it, the equation behind it, and a worked example.

How to use it

1. Enter the air temperature in Celsius, Fahrenheit, or kelvin.
2. Press Calculate for the speed of sound, which you can read in metres per second and other units, or Reset to clear it.
3. Or use the reference dropdown to look up a tabulated speed at a chosen temperature.

What the speed of sound is

The speed of sound is how fast a sound wave travels through a medium, in this case air. A sound is a wave of pressure, a pattern of slight compressions and rarefactions passing from one patch of air to the next, and the speed of sound is the pace at which that pattern moves outward from its source. In ordinary air, that pace is about 343 metres per second, which is fast by everyday standards but far slower than light.

That gap between the speed of sound and the speed of light is something you notice all the time. You see a distant firework burst before you hear it, watch a hammer strike land before the clang reaches you, and see lightning before thunder. In each case the light arrives almost instantly while the sound takes its time, and the delay is a direct sign of how comparatively slowly sound travels. The calculator pins down that speed for any air temperature.

Why temperature is what matters

For sound in air, temperature is the dominant influence on the speed, more than pressure or anything else. The reason lies in how sound propagates: the wave moves by air molecules bumping into their neighbours and passing the disturbance along. Warmer air has faster-moving molecules, so they collide and relay the wave more quickly, and the speed of sound rises. Cooler air has slower molecules, and sound travels more slowly through it.

The effect is steady and predictable: the speed of sound increases by roughly 0.6 metres per second for every degree Celsius of warming. So sound travels noticeably faster on a hot summer afternoon than on a freezing winter night. Air pressure, by contrast, has almost no effect, because raising the pressure packs the molecules closer but also makes the air heavier in exactly the offsetting amount. This is why the calculator needs only the temperature to give the speed of sound in air.

The equation it uses

The calculator uses the physics of sound in an ideal gas, which gives the speed from the absolute temperature:

c = √( γ R T ÷ M )

Here T is the absolute temperature, R is the gas constant, M is the molar mass of air, and γ is the adiabatic index of air, about 1.4, which reflects how air heats slightly as the sound wave compresses it. Since everything except the temperature is fixed for air, the speed depends only on the square root of the absolute temperature. This is why the dependence on temperature, though real and steady, is fairly gentle: it takes a fourfold rise in absolute temperature to double the speed of sound.

Sound in other materials

Air is only one medium, and sound travels at very different speeds through others. As a rule, sound moves slowest through gases, faster through liquids, and fastest through solids, because the more tightly packed and stiffly bound the particles are, the more quickly they pass a disturbance along. In water, sound travels at around 1,480 metres per second, more than four times its speed in air, which is why whales can communicate across vast stretches of ocean. In steel it is faster still, several thousand metres per second.

The calculator focuses on air, where temperature is the key variable, and its reference dropdown lists tabulated speeds for comparison. The broad lesson is that the speed of sound is a property of the medium as much as of the sound itself: the same shout would race away far quicker through a steel rail than through the air around it, which is why you can sometimes hear an approaching train through the track before you hear it through the air.

Units and precision

The calculator takes the temperature in Celsius, Fahrenheit, or kelvin, converting to absolute temperature internally, and reports the speed of sound in metres per second along with kilometres per hour, feet per second, miles per hour, knots, and feet per minute. It uses the standard values of the gas constant, the molar mass of air, and the adiabatic index, so the result is an accurate figure for dry air at the given temperature. Results carry several significant figures.

A worked example

Take air at 20 degrees Celsius, a comfortable room temperature.

The speed of sound works out to about 343 metres per second, the familiar textbook value. Cool the air to 0 degrees and it falls to about 331 metres per second; warm it to 35 degrees and it rises to about 352 metres per second. Across that whole range the change is only a few percent, which shows how gently the speed of sound responds to temperature, even though the dependence is real and measurable.

Questions people ask

What is the speed of sound in air?

About 343 metres per second in dry air at 20 degrees Celsius. It rises with temperature, reaching about 331 metres per second at 0 degrees and about 352 at 35 degrees.

Why does the speed of sound depend on temperature?

Because sound travels by molecules colliding and passing the wave along. Warmer air has faster molecules that relay the disturbance more quickly, so the speed rises by about 0.6 metres per second per degree Celsius.

Does air pressure change the speed of sound?

Almost not at all. Raising the pressure packs the molecules closer but makes the air correspondingly heavier, and the two effects cancel, leaving temperature as the dominant factor.

Why is sound faster in water and solids?

Because their particles are more tightly bound, so a disturbance passes along more quickly. Sound is slowest in gases, faster in liquids, and fastest in solids, travelling several times quicker in water than in air.

References

A quick note on where the physics comes from. The speed of sound in air and its dependence on temperature are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The reference values follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 1, Section 17.2, Speed of Sound. https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound
2. HyperPhysics, Speed of Sound in Air. http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811