Sonic Velocity Calculator

Gas

Gas types with pre-calculated gamma × R products for sonic velocity calculation

Temperature

Sonic velocity (speed of sound)

Pick a gas and enter a temperature to get the speed of sound. Or enter a measured sonic velocity and leave the temperature blank to work out the temperature of the gas.

Show the Mach number

Enter the speed of an aircraft or a gas flow to get its Mach number, the ratio of that speed to the local speed of sound, and see which flight regime it falls in: subsonic, transonic, supersonic or hypersonic.

Use a custom gas

Define your own gas by its heat-capacity ratio (Cp/Cv) and molecular weight instead of picking a preset. Handy for gas mixtures, steam or any gas not in the list. Also shows the choked-flow critical pressure ratio.

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Show the speed-versus-temperature curve

Plot how the speed of sound in the selected gas rises with temperature, from a deep freeze to a hot day, so you can read off the value anywhere on the curve.

Compare the gases

Compare the speed of sound across air, helium, hydrogen and the other gases at your temperature, as a bar chart and a table of their heat-capacity ratio, molecular weight and sound speed.

Sound is a pressure wave and its propagation speed depends on the medium and its temperature. This calculator allows you to calculate the speed of sound in air or other gases at any given temperature. Select a gas, enter the temperature and check the result. Conversely, you can also input a measured sound velocity and have it compute the temperature.

What is the speed of sound?

The speed of sound is the rate at which a small pressure disturbance propagates through a gas. When you clap, one air molecule pushes on its neighbor and that force is felt as sound and transmitted outward. This speed depends on properties of the gas, in particular its stiffness (expressed by the ratio of heat capacities) and molecular mass (expressed by molar mass).

In fluid mechanics this value has a different meaning. The speed of sound is the maximum velocity that a gas can reach when flowing through pipes, nozzles or valves. Although an increased pressure difference on either side of an opening will increase flow rate, it only does so up to the speed of sound. At this point there is choking and the flow cannot get any faster; hence why it's also called critical velocity. This upper limit is important when selecting safety or control valves.

Formula:

For ideal gases the speed of sound is equal to the square root of the product of the ratio of specific heats, the specific gas constant, and the absolute temperature.

c = \sqrt{\gamma \, R \, T}

Here 'c' is the speed of sound, the Greek letter gamma represents the ratio of specific heats, Cp and Cv (also called the adiabatic exponent). R is the specific gas constant for the gas, and T is the absolute temperature in Kelvin. The specific gas constant is obtained by dividing the universal gas constant by the molar mass. So: the lighter the gas, the larger R is, and the speed of sound is higher.

The formula can be directly derived from the following: Since only absolute temperature appears in the formula, sound speed increases proportionally to the square root of temperature. In an ideal gas, sound speed is not dependent on pressure. The lighter the molecules are, the larger R is. Therefore, sound speed is higher for helium and hydrogen, and lower for carbon dioxide.

Example calculation:

Let's take air at 25 degrees Celsius as an example. First we convert it to absolute temperature. If we add 273.15 to 25, we get 298.15 Kelvin. Since air is mainly made up of the diatomic molecules nitrogen and oxygen, the ratio of heat capacities is about 1.4, and the specific gas constant is 287 Joules per kilogram and Kelvin. If you multiply gamma by R, you get 401.8. This is the value that the calculator stores for this air.

c = \sqrt{401.8 \times 298.15} = \sqrt{119{,}797} \approx 346.1 \ \text{m/s}

This means that the speed of sound is 346 meters per second which is equivalent to 1246 kilometers or 774 miles per hour. This is the speed of sound at room temperature in everyday life. If we heat up air to 35 degrees, then the speed of sound increases to about 352 meters per second and if we cool it down to 5 degrees, then it decreases to about 334 meters per second.

Backwards calculation.

The formula relates temperature and speed so the calculation is just as easy going the other way. If you enter the speed of sound and leave the temperature field blank then the calculator will re-arrange the formula to calculate the temperature of the gas. There is no need for a switch, simply leaving one field blank tells the calculator to perform the calculation in the opposite direction.

To find	Rearranged formula	In words
Sonic velocity	$c = \sqrt{\gamma R T}$	From the gas and the temperature
Temperature	$T = \dfrac{c^2}{\gamma R} - 273.15$	From the gas and a measured sound speed

Converting sound speed to temperature is not just a theoretical exercise. Sound velocity meters measure the time it takes for sound to travel short distances and use that to calculate air temperature. They can take multiple measurements per second and respond faster than any traditional thermometer.

Why gases are important.

Even if the temperature is the same, sound speed can vary by a factor of many times depending on the type of gas. At room temperature, the speed of sound in helium is about 1007 meters per second, which is almost three times faster than the speed of sound in air. This is because helium atoms are on average seven times lighter than typical air molecules. When you inhale a small amount of helium, your voice sounds higher not because the pitch of your vocal cords changes but because the faster sound speed increases the resonant frequencies of your vocal tract. Carbon dioxide is heavy and moves slowly, so the speed of sound in it is only about 267 meters per second, and inhaling large amounts of carbon dioxide results in a lower voice.

If you activate the gas comparison function, you can see how fast sound travels at a given temperature through air, helium, hydrogen, nitrogen, oxygen, carbon dioxide and argon.

Mach number.

The Mach number is the ratio of speed to sound speed at that location and it is the most important single measure for high-speed flight. Mach 1 corresponds exactly to the speed of sound, while Mach 2 corresponds to twice the speed of sound. The speed of sound decreases with decreasing temperature, which is why air in great height is much colder and the Mach number at the same true approach speed in cruising altitude is higher than at sea level. Flows below Mach 0.8 are subsonic, while approaching Mach 1 first shock waves form, above that it's a supersonic flow and above Mach 5 a hypersonic flow. With the activation of the Mach layer any input speeds can be classified.

Choked flow and critical pressure ratio

When a gas flows through an orifice or valve, it is accelerated by the pressure drop across the flow. However, when the pressure ratio on either side of the opening reaches a certain value, the flow area becomes "choked" and reaches the speed of sound. Further reduction in downstream pressure will not result in further acceleration. This threshold value is known as the critical pressure ratio, and depends only upon the ratio of specific heats.

\frac{p^*}{p_0} = \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma}{\gamma - 1}}

For air with a heat capacity ratio of 1.4, the calculated result is about 0.528, which also explains the rule of thumb that flow separation occurs when the inlet pressure is approximately twice as high as the outlet pressure. In the custom gas layer this ratio is specified for each defined gas.

When the ideal assumption no longer applies

This formula assumes an ideal gas. This is a very good approximation for everyday air and gases at temperatures near room temperature with deviations usually within a few percent. At extremely high pressures the molecules are compressed to densities similar to those of liquids, so this approximation no longer holds true. When the gas approaches its condensation temperature, it becomes less accurate. In humid air, sound travels slightly faster because water vapor weighs less than dry air, but the increase is only a few tenths of a percent at most. For precise calculations you should use the measured heat capacity ratio and gas constant appropriate for your particular gas and conditions.

Frequently asked questions

What is the speed of sound in air?

At 20 degrees Celsius, the speed of sound in dry air is about 343 meters per second, which is approximately 1,236 kilometers per hour or 767 miles per hour. However, this is not a fixed value. The speed of sound is about 349 meters per second at a temperature of 30 degrees Celsius and decreases to about 331 meters per second at a temperature of 0 degrees Celsius. For ideal gases, the speed of sound does not depend on the pressure of the air.

How does the speed of sound change with temperature?

Since the speed of sound is proportional to the square root of absolute temperature, gases at higher temperatures transmit sound more quickly. When the temperature increases from 0 degrees Celsius to 20 degrees Celsius, the speed of sound in air increases from about 331 meters per second to 343 meters per second. A practical approximation for air is: Add 331.3 to the value obtained by multiplying the temperature in degrees Celsius by 0.606. The result is expressed in meters per second.

Why does sound travel faster through helium than air?

Sound travels faster in lighter gases. The helium atoms are about seven times lighter than the average air molecule, so the specific gas constant for helium is much larger and the speed of sound is about three times that in air, reaching nearly 1000 meters per second at room temperature. This is why your voice gets higher when you take a breath of helium.

What is a mach number?

The Mach number is the ratio of speed to local speed of sound. Thus a Mach number of 1 exactly corresponds to the speed of sound and a Mach number of 2 is twice the speed of sound. As the speed of sound depends on temperature and altitude, at the same flight speed the Mach numbers are different at sea level and cruise altitude. Below a Mach number of 0.8 the flow state is subsonic, approaching Mach 1 it becomes transonic, above that it is supersonic and above Mach 5 it is hypersonic.

Can this calculator be used for liquids or solids?

No. This calculator models an ideal gas where the speed of sound is equal to the square root of gamma times R times T. For liquids and solids, the speed of sound is the ratio of the bulk modulus over the square root of density and it's much higher. In water, it's about 1480 meters per second, in steel, it's over 5000 meters per second.

What is the speed of sound in compressible flows?

In fluid dynamics the speed of sound is the maximum speed that a gas can reach when flowing through an orifice or valve. When the pressure ratio across an opening reaches a critical value (about 0.528 for air), then the gas will flow at sonic velocity. No matter how much backpressure is reduced, the flow cannot be accelerated further. This corresponds to the same speed of sound but from the perspective of the stream and limits the choices for safety valves.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Speed of sound
The speed of sound in gases, the ideal-gas formula c = sqrt(gamma R T), and its dependence on temperature and molecular weight.
Engineering ToolBox: Speed of Sound Equations
Sonic velocity in gases, fluids and solids, with the ideal-gas and bulk-modulus forms and worked values.
Wikipedia: Choked flow
The critical pressure ratio at which compressible flow reaches sonic velocity and chokes.