The speed of sound calculator above gives the propagation speed of a sound wave in the medium you specify. In air it works from the temperature you enter and corrects for humidity, which most calculators ignore. In any other gas it works from the heat capacity ratio and the molar mass. In a solid or a liquid it works from the elastic modulus and the density, which is the same physics arriving through a different door.
Arb Digital builds free physics calculators that own one job properly rather than burying it inside another. Several tools on this site need the speed of sound internally — the Doppler calculator derives it from temperature, and the Mach number calculator does the same — but neither exposes it as the answer or lets you change the medium. This page does both.
What This Speed of Sound Calculator Does
Sound is a pressure wave, and how fast it travels is set by two competing properties of the medium: how stiff it is, which makes disturbances propagate faster, and how dense it is, which makes them propagate slower. Every formula on this page is a version of the square root of stiffness divided by density. In a gas the stiffness is supplied by the pressure and the thermodynamics of compression; in a solid it is supplied by the elastic modulus.
The result is given in metres per second, with the grid converting it to kilometres per hour and miles per hour, giving the wavelength at a frequency you choose, and giving the propagation delay over a hundred metres. That last figure is the most practical one on the page for anybody working with distributed loudspeakers or microphone arrays, where a few metres of path difference is an audible delay.
In air mode the tool also reports how much of the answer comes from the humidity, because that contribution is small, real, and almost universally left out. Moist air is slightly less dense than dry air at the same temperature and pressure, since a water molecule is lighter than the average air molecule it replaces, and sound therefore travels marginally faster through it.
How to Use It
- Pick the medium first. The three modes use different inputs and different formulas, and only the boxes relevant to your choice are read.
- For air, enter the temperature accurately. It is the dominant input by a wide margin. Humidity and pressure are refinements worth a fraction of a per cent between them.
- For another gas, set γ and the molar mass. Both are properties of the gas rather than of the conditions, and both are published for every common gas.
- For a solid or liquid, choose the right modulus. Young's modulus gives the speed along a thin rod. The bulk modulus gives the speed through a large body of liquid or bulk solid. They can differ by tens of per cent for the same material.
- Read the wavelength if you are working with acoustics. Wavelength, not frequency, is what determines whether an object diffracts sound around itself or blocks it.
The Formula: How the Speed of Sound Is Calculated
For an ideal gas the speed is c = √(γRT ÷ M), where γ is the ratio of specific heats, R is the universal gas constant of 8.314463 J/(mol·K), T is the absolute temperature in kelvin and M is the molar mass in kilograms per mole. NASA Glenn's page on the role of the Mach number gives this relation in the equivalent form a² = γRT using the specific gas constant, and explains why the speed of sound is the speed at which small isentropic disturbances travel.
The familiar schoolroom version, c = 331.3 × √(1 + TC ÷ 273.15), is that same expression with air's γ and molar mass already substituted. OpenStax University Physics Volume 1, section 17.2 on the speed of sound, derives it and notes the 343 m/s result at 20 °C.
The humidity correction works by replacing dry air's molar mass and heat ratio with mixture values. The tool computes the saturation vapour pressure at your temperature, multiplies by the relative humidity to get the actual vapour pressure, divides by the total pressure to get the mole fraction of water vapour, and then mixes the two gases' properties in that proportion. Water vapour has a molar mass of 18 g/mol against dry air's 28.96, so adding it lightens the mixture and speeds the sound up.
For a solid or a liquid the thermodynamic route is replaced by the elastic one: c = √(E ÷ ρ) along a thin rod, or √(K ÷ ρ) for a bulk fluid, where E is Young's modulus, K is the bulk modulus and ρ is the density. Reference data for fluid properties is available from the NIST Chemistry WebBook thermophysical properties of fluid systems, which is where a defensible bulk modulus and density for a working fluid should come from.
Work the defaults. At 20 °C, 50 per cent humidity and standard pressure, the vapour mole fraction is about 0.0115, giving a mixture molar mass of 28.839 g/mol and a γ of 1.3992. Then c = √(1.3992 × 8.314463 × 293.15 ÷ 0.028839) = √(118,259) = 343.9 m/s. Dry air at the same temperature gives 343.2 m/s, so humidity has contributed about 0.7 m/s.
Why Pressure and Altitude Do Not Change the Answer
This is the single most persistent misconception in the subject. The speed of sound in air is independent of pressure. Raising the pressure makes the air stiffer, which speeds sound up, and denser by exactly the same proportion, which slows it down, and the two effects cancel completely for an ideal gas.
So why do aviation tables show the speed of sound falling with altitude? Because temperature falls with altitude. In the troposphere the standard atmosphere loses about 6.5 °C per kilometre, and it is that cooling, not the thinning air, that drops the speed of sound from 340 m/s at sea level to about 295 m/s at the tropopause. Enter the temperature at altitude in this tool and you get the aviation figure without touching the pressure box.
Pressure appears in the air mode here for one narrow reason: the mole fraction of water vapour at a given relative humidity depends on the total pressure. That is a second-order effect on a second-order correction, and it will never move the answer by more than a fraction of a metre per second.
Why Sound Is So Much Faster in Solids
Sound travels at roughly 343 m/s in air, 1,480 m/s in fresh water and around 5,000 m/s along a steel bar. The obvious guess — that denser materials carry sound faster — is exactly backwards, since density is in the denominator. What actually dominates is stiffness. Steel is about 8,000 times denser than air, which alone would make sound 90 times slower, but its elastic modulus is roughly a million times larger, and the stiffness wins comfortably.
That competition explains a result that looks strange at first: sound travels faster in a light stiff material such as beryllium than in a dense stiff one such as lead, and faster in helium than in air even though both are gases at the same temperature. Helium's molar mass is seven times smaller than air's, and the square root of that ratio is most of the reason a lungful of it raises your voice.
It also explains why the modulus you pick matters. A thin rod is free to expand sideways when compressed, so it resists with Young's modulus. A large block cannot, so it resists with a stiffer combination, and bulk longitudinal waves travel faster than rod waves in the same material. Using the wrong one is a real error of ten to twenty per cent.
Where This Sits Next to the Other Wave Tools
Several tools on this site use the speed of sound as an intermediate step. The Mach number calculator derives it from temperature to divide a speed by it, and the Doppler effect calculator derives it to work out a frequency shift. Neither lets you choose a gas or a solid, and neither reports the speed as the answer. This page owns the standalone calculation across every medium, and the other two are the right tools once you need what happens to a wave rather than how fast it goes.
Alongside them, the wavelength calculator converts between frequency and wavelength for any wave speed, the sound attenuation calculator handles how the level falls with distance, and the decibel calculator handles the level arithmetic itself. For the inputs, the relative humidity calculator and the air density calculator pin down the state of the air, and the speed converter moves the answer into whatever units you need.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating 343 m/s as a constant — that is the value at 20 °C only, and the speed moves by about 0.6 m/s for every degree Celsius.
- Assuming pressure or altitude changes the speed directly — for an ideal gas the stiffness and density effects cancel exactly. Altitude matters only through temperature.
- Using Young's modulus for a bulk solid — the rod formula applies only when the material is free to expand sideways. In a large body the bulk longitudinal speed is higher.
- Using Celsius directly in the gas formula — the thermodynamic relation needs absolute temperature. Forgetting to convert to kelvin produces a wildly wrong answer.
- Assuming the speed depends on frequency — in air and water it does not, to a very good approximation. Dispersion exists but is negligible across the audible range.
Related Free Tools From Arb Digital
Take this speed into the Mach number calculator for aerodynamics, the Doppler effect calculator for a moving source, and the wavelength calculator for wave geometry. For level rather than speed, use the sound attenuation calculator and the decibel calculator. On the input side, the relative humidity calculator and the air density calculator describe the air itself, and the speed converter handles units. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
About 343 metres per second in dry air at 20 degrees Celsius, which is roughly 1,235 kilometres per hour or 767 miles per hour. At 0 degrees Celsius it drops to about 331 metres per second, and the change is close to 0.6 metres per second per degree.
No, not for an ideal gas. Higher pressure makes the air stiffer and denser in exactly the same proportion, and the two effects cancel in the square root. This is why the speed of sound is the same at the top of a mountain as at sea level for the same air temperature.
Less than a per cent in ordinary conditions. At 20 degrees Celsius, going from completely dry to saturated raises the speed by around 1 metre per second out of 343. It grows with temperature because warm air can hold far more vapour, but it never becomes a large effect.
Because sound travels about three times faster in helium than in air, which raises the resonant frequencies of your vocal tract. The pitch your vocal cords produce does not change at all; what changes is which harmonics the tract emphasises, so the timbre shifts rather than the fundamental.
Because water is far stiffer relative to its density. It is about 800 times denser than air, which on its own would slow sound down, but its bulk modulus is roughly 15,000 times larger. Stiffness wins, and sound travels at about 1,480 metres per second in fresh water.
Young's modulus for a long thin rod or bar, where the material can expand sideways as it is compressed. The bulk longitudinal case, appropriate to a large body of material, gives a higher speed. Mixing the two up is a genuine error of ten to twenty per cent.
Essentially no in air and water across the audible range. Media where wave speed varies with frequency are called dispersive, and air's dispersion is far too small to matter for ordinary acoustics. It becomes significant only at ultrasonic frequencies or in strongly absorbing media.
This tool is provided for educational and study use. It models ideal gas behaviour and simple elastic wave propagation, and does not account for dispersion, extreme pressures, non-ideal gas behaviour or anisotropic materials, so treat its output as a physics result rather than a calibrated measurement.
