Speed of Sound Calculator

Check with our speed of sound calculator how the speed of sound in water or air changes with temperature.

Speed of sound in air343.235 m/s√(γRT/M) with γ = 1.4 and M = 28.9647 g/mol

Independent of pressureyespressure and density change together and cancel, so only temperature matters — this is why the speed of sound is constant through the isothermal stratosphere

The linear approximation343.42 m/s331.3 + 0.606T(°C) — accurate to a fraction of a percent over normal temperatures

Air density here1.20411 kg/m³

Acoustic impedance of air here413.29 Pa·s/mabout 413 at room temperature

At 10 K warmer349.04 m/sthe speed goes as the square root of ABSOLUTE temperature, so a 10 K rise near room temperature adds under 2%

Travel time over 340 m990.575 ms

Wavelength of a 440 Hz tone780.0795 mmconcert A — wavelength scales with the medium's speed, which is why instruments must be retuned as a hall warms

The formula

gas c = √(γRT/M); solid rod c = √(E/ρ)

Temperature, not pressure

The speed of sound in a gas is √(γRT/M), which contains temperature but not pressure. Pressure and density appear in the underlying relation as a ratio and cancel exactly, so taking a gas up a mountain does not slow its sound — only cooling it does. This is why the speed of sound falls through the troposphere and then holds steady through the isothermal stratosphere while the pressure keeps dropping.

Molar mass is the other lever. Helium's 4 g/mol against air's 29 makes sound nearly three times faster in it, which is what changes a voice. The vocal folds still vibrate at the same rate — the pitch is unchanged — but the vocal tract's resonances scale with the speed of sound and all shift upward, altering the timbre. Describing it as raising the pitch is wrong.

In solids the relevant relation is √(E/ρ), giving speeds of several kilometres per second. The huge acoustic impedance mismatch with air means almost all sound reflects at the boundary rather than crossing it — which is simultaneously why sound travels so far along a rail and why so little of it reaches your ear through the air.