Speed of Sound Calculator

Sound travels as a longitudinal pressure wave through a medium. In an ideal gas, the speed of sound depends on temperature according to the exact formula:

$$v = \sqrt{\gamma \cdot R \cdot T / M}$$

where $$\gamma = 1.4$$ is the adiabatic index for air, $$R = 8.314 \text{ J/(mol·K)}$$ is the gas constant, $$T$$ is absolute temperature in Kelvin, and $$M = 0.029 \text{ kg/mol}$$ is the molar mass of air.

For practical calculations in the range of typical atmospheric temperatures, this simplifies to the well-known linear approximation:

$$v = 331.3 + 0.606 \cdot T_C \text{ m/s}$$

where $$T_C$$ is the temperature in degrees Celsius. The constant 331.3 m/s represents the speed of sound at 0°C, and the coefficient 0.606 accounts for the temperature dependence. This approximation is accurate to within 0.1% for temperatures between -30°C and 50°C.

The calculator converts the result into feet per second (multiply by 3.28084), miles per hour (multiply by 2.23694), and kilometers per hour (multiply by 3.6) for convenience in different fields.

At standard room temperature (20°C), sound travels at approximately 343.2 m/s or about 1,125 ft/s. As temperature increases, air molecules move faster, transmitting the pressure wave more efficiently. At freezing (0°C), sound speed drops to 331.3 m/s. In hot desert conditions (45°C), it rises to about 358.6 m/s. These variations matter significantly in precision applications like sonar, acoustic measurements, and musical instrument tuning.