Last updated: 2026-06-15

Speed of Sound in Air

Sound is a mechanical wave — a chain of pressure fluctuations that propagates through a medium by pushing neighbouring molecules together and apart. In a gas such as air, the speed at which this wave travels depends on how quickly molecules can transfer momentum, which is determined primarily by their temperature. The higher the temperature, the faster the molecules move, and the more rapidly the pressure wave advances.

This calculator gives the speed of sound in dry air for any temperature between absolute zero and whatever upper limit your application requires.

How temperature governs the speed

The kinetic theory of gases gives an exact relationship between the speed of sound $v$ and the absolute temperature $T$ (in kelvin):

$v = 331.3 \cdot \sqrt{\frac{T}{273.15}} \quad \text{m/s}$

The constant 331.3 m/s is the measured speed at 0 °C (273.15 K). Near room temperature the square-root formula is well approximated by the simpler linear rule:

$v \approx 331.3 + 0.6 \cdot T_{\!\circ\text{C}} \quad \text{m/s}$

meaning the speed increases by about 0.6 m/s for every degree Celsius rise in temperature. The calculator uses the exact square-root formula for accuracy across the full temperature range.

Formula table

Worked example

What is the speed of sound on a warm summer day at 35 °C?

Convert to kelvin: $T = 35 + 273.15 = 308.15\ \text{K}$.

$v = 331.3 \cdot \sqrt{\frac{308.15}{273.15}} = 331.3 \cdot \sqrt{1.1282} = 331.3 \times 1.0622 \approx 351.9\ \text{m/s}$

This is roughly 1,267 km/h (787 mph). By comparison, at 20 °C the speed is:

$v = 331.3 \cdot \sqrt{\frac{293.15}{273.15}} \approx 343.2\ \text{m/s}$

— an increase of almost 9 m/s between 20 °C and 35 °C, consistent with the 0.6 m/s per °C rule of thumb.

Practical context

The Mach number is defined as the ratio of an object's speed to the local speed of sound. At sea level on a standard day (15 °C) the speed of sound is about 340 m/s (1,225 km/h), so Mach 1 corresponds to roughly 1,225 km/h. At high altitude, where air is colder, the speed of sound is lower and Mach 1 corresponds to a slower airspeed — an important consideration in aviation.

Humidity has a small positive effect on the speed (water vapour is lighter than the nitrogen–oxygen mix it displaces), but the effect is less than 1 m/s under typical conditions and is not included here.

Limitations

This formula applies to dry air. Other gases have different values of the heat-capacity ratio $\gamma$ and the molar mass $M$, so their speed-of-sound equations differ. Sound also travels much faster in liquids and solids: about 1,480 m/s in water and 5,100 m/s in steel. For those media a separate formula based on the bulk or Young's modulus is required.