CalculateY
Quick Answer
At 20 degrees Celsius, the speed of sound in air is approximately 343.2 m/s (1,235.5 km/h). At 0 degrees C, it is approximately 331.3 m/s.
Speed of sound in air
Mach number
Enter an object's speed to calculate its Mach number at the temperature above.
Speed of sound in common media
Common Examples
| Input | Result |
|---|---|
| Temperature = 0 C | 331.30 m/s (1,192.68 km/h) |
| Temperature = 20 C | 343.21 m/s (1,235.56 km/h) |
| Temperature = -40 C | 306.18 m/s (1,102.24 km/h) |
| Object at 400 m/s, air at 20 C | Mach 1.17 (transonic) |
| Speed of sound in steel | 5,960 m/s (21,456 km/h) |
How It Works
This calculator uses the standard approximation for the speed of sound in an ideal gas:
\[v = 331.3 \times \sqrt{1 + \frac{T}{273.15}}\]Where:
- v = speed of sound in meters per second (m/s)
- T = air temperature in degrees Celsius
- 331.3 m/s = speed of sound at 0 degrees C
- 273.15 = offset to convert Celsius to Kelvin
This formula is derived from the more general expression v = sqrt(gamma * R * T_K / M), where gamma is the adiabatic index (1.4 for air), R is the universal gas constant, T_K is absolute temperature in Kelvin, and M is the molar mass of air. Because gamma, R, and M are constants for dry air, the formula simplifies to the square root form above.
Unit conversions
- Feet per second: multiply m/s by 3.281
- Kilometers per hour: multiply m/s by 3.6
- Miles per hour: multiply m/s by 2.237
- Knots: multiply m/s by 1.944
Mach number
The Mach number is the ratio of an object’s speed to the local speed of sound:
\[M = \frac{v_{\text{object}}}{v_{\text{sound}}}\]Flight regimes based on Mach number:
| Regime | Mach range |
|---|---|
| Subsonic | Below 0.8 |
| Transonic | 0.8 to 1.2 |
| Supersonic | 1.2 to 5.0 |
| Hypersonic | Above 5.0 |
Why temperature matters
Sound is a pressure wave that propagates through the vibration of air molecules. At higher temperatures, molecules move faster and transfer energy more quickly, so sound travels faster. Each 1 degree C increase raises the speed of sound by roughly 0.6 m/s near room temperature.
Speed of sound in other media
Sound generally travels faster in denser, stiffer materials. In water at 20 degrees C, the speed is approximately 1,482 m/s, about 4.3 times faster than in air. In steel, it reaches approximately 5,960 m/s. The reference table in the calculator lists values for common gases, liquids, and solids.
Worked example
At 15 degrees C (a typical outdoor temperature), the speed of sound is v = 331.3 * sqrt(1 + 15/273.15) = 331.3 * sqrt(1.0549) = 331.3 * 1.02707 = 340.27 m/s. That is approximately 1,224.97 km/h or 761.0 mph. A commercial jet flying at 250 m/s in these conditions has a Mach number of 250 / 340.27 = 0.735, which falls in the subsonic regime.