What this calculator does
Find out how fast sound travels through air, or through any other gas, at the temperature you choose. Sound is a pressure wave passed from molecule to molecule. So its speed depends on how fast those molecules move. In a gas, that's set mainly by temperature: warm air carries sound faster than cold air. Near room temperature, sound moves through air at about 343 meters per second. That's roughly a kilometer every three seconds, or a mile every five.
This calculator offers two methods. The dry-air method needs only the temperature. The general method uses the ideal-gas formula. It needs the gas's heat capacity ratio, γ (gamma), and its molar mass, M (how much a fixed number of its molecules weighs). So it works for helium, carbon dioxide, pure nitrogen or any other gas that behaves like an ideal gas.
Where it's used
Why this math matters outside the classroom:
- Lightning distance. Counting the seconds between lightning and thunder and dividing by about 3 gives the storm's distance in kilometers.
- Warm concert halls. Musicians find wind instruments go slightly sharp in a warm hall, since sound travels faster in warmer air.
- Room temperature. At 20 °C, sound in dry air travels at about 331.3 × √(1 + 20 ÷ 273.15) ≈ 343 m/s.
- Hall acoustics. Acoustic engineers time echoes in a concert hall to work out the delays from walls and ceiling.
- Mach number. Pilots know Mach 1 is a lower speed at cruising altitude because the air there is much colder.
How to use it
- Choose dry air, or any ideal gas if you want to enter γ and the molar mass yourself.
- Enter the temperature in Celsius, Fahrenheit or kelvins.
- For the general method, enter γ and the molar mass in grams per mole.
- Choose the unit for the answer. Travel times for one kilometer and one mile are listed too.
What the inputs mean
- Heat capacity ratio (γ)
- The heat capacity ratio γ = cp/cv tells how strongly a gas's pressure rises when it's squeezed quickly. Gases of single atoms have γ = 5/3. Gases of two-atom molecules, such as N₂ and O₂, have about 1.40. Larger molecules have lower values.
- Molar mass (M)
- The mass of one mole of the gas (a mole is a fixed, very large count of molecules). Dry air is a mixture, with an average of about 28.96 g/mol. Lighter gases carry sound faster.
Formula and method
Dry air: v = 331.3 × √(1 + T ÷ 273.15) (T in °C, v in m/s) Any ideal gas: v = √(γ × R × T ÷ M) (T in K, M in kg/mol) R = 8.314462618 J/(mol·K)
v is the speed of sound and T is the temperature. γ is the heat capacity ratio, M is the molar mass and R is the gas constant, a fixed number from physics.
The dry-air formula starts with the speed at 0 °C, 331.3 m/s. Then it scales that by the square root of a ratio: the air's temperature over the freezing point, both on the kelvin scale (which starts at absolute zero). 1 + T/273.15 equals T(K) ÷ 273.15. So sound speed grows with the square root of the kelvin temperature.
The general formula treats a sound wave as quick squeezes of an ideal gas, too fast for heat to flow in or out (physicists call this adiabatic). Pressure and density don't appear separately. For an ideal gas at a fixed temperature, they rise and fall together. Both methods ignore humidity.
Worked example
How fast does sound travel through dry air at 20 °C?
- v = 331.3 × √(1 + 20 ÷ 273.15) = 331.3 × √1.07322 = 343.21 m/s.
- Time to cover 1 km: 1,000 ÷ 343.21 = 2.914 s.
Result: Sound travels at about 343.21 m/s (1,235.6 km/h or 767.7 mph), covering a kilometer in about 2.9 seconds.
Understanding the result
Each degree Celsius adds roughly 0.6 m/s near room temperature. On a −20 °C winter day, sound moves at about 319 m/s. On a 35 °C summer afternoon, it's about 352 m/s.
The two methods agree within about 0.1 m/s for air. That's because 331.3 m/s is itself what the ideal-gas formula gives for air at 0 °C. Use the general method for any other gas.
This speed is also Mach 1 for the conditions you entered. That's why an aircraft's Mach number depends on the temperature at its altitude.
Assumptions and limitations
- The gas is dry and behaves as an ideal gas.
- γ stays the same over the temperature range. That holds well for air from about −50 °C to 150 °C.
- The sound is of ordinary loudness, not a shock wave.
- Humidity is ignored. Moist air is slightly lighter, so sound travels a little faster. It's typically under 0.5% faster at room temperature, and more in hot, humid air.
- Liquids and solids follow different formulas based on stiffness and density. They aren't covered here.
- At very high temperatures, γ itself falls. So the general formula gives too high a speed unless you enter the γ for that temperature.
Frequently asked questions
Does air pressure change the speed of sound?
Not for an ideal gas at a fixed temperature. Higher pressure makes air both stiffer and denser by the same amount, so the effects cancel. Sound is slower at high altitude because the air there is colder, not because it's thinner.
Why does helium make voices sound higher?
Helium's molar mass is about one-seventh that of air, so sound travels nearly three times faster in it. The natural ringing tones of your throat and mouth shift upward, which changes the tone of your voice. Your vocal cords still vibrate at much the same pitch.
How far away was the lightning?
Count the seconds between the flash and the thunder, and multiply by the speed of sound. At 20 °C, that's about 343 m per second. So 3 seconds is about 1 km, and 5 seconds is about 1 mile.
Why 331.3 m/s at 0 °C?
It's the value most often quoted, both measured and calculated, for dry air at the freezing point. The ideal-gas formula with γ = 1.4 and M = 28.9647 g/mol gives 331.32 m/s, a close match.
How this calculator is checked
Method: Laplace's adiabatic sound speed v = √(γRT/M) for an ideal gas; dry-air approximation v = 331.3√(1 + T/273.15) m/s; R = 8.314462618 J/(mol·K). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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