Speed of Sound in a Medium Calculator

How it is calculated

The speed of a sound wave in a fluid or solid is v = √(K ÷ ρ), where K is the elastic (bulk) modulus in pascals (Pa) and ρ is the density in kg/m³. The result is in metres per second. The tool also converts it: km/h is v × 3.6, mph is v × 2.23694, and the Mach figure is v ÷ 343, so Mach here is relative to the speed of sound in air at 343 m/s, not to the medium itself. Both inputs must be above zero. Enter the modulus in Pa, not GPa: a value like 2.2e9 or 2200000000 is accepted. For a thin solid rod, use Young's modulus as K; for a liquid or a gas, use the bulk modulus. The formula does not include temperature, so enter the modulus and density that apply at your temperature.

Common mistakes

• Entering the modulus in GPa or MPa. The field is in pascals, so typing 2.2 for 2.2 GPa gives about 0.05 m/s instead of 1,483 m/s. Convert to Pa first.
• Entering the density in g/cm³. It must be kg/m³: water is 1000, not 1.
• Using Young's modulus for a liquid or gas, or the bulk modulus for a thin rod. Pick the modulus that matches how the wave moves in your medium.
• Reading the Mach figure as relative to the medium. It is always divided by 343 m/s, the speed of sound in air.
• Ignoring temperature. The modulus and density change with it, and so does the speed; use values for the temperature you care about.