How to use the speed of sound calculator
- Enter the air temperature and choose Celsius, Fahrenheit or kelvin.
- Read the speed of sound in meters per second, kilometers per hour, miles per hour, feet per second and knots.
- Open the advanced options and enter a frequency to see the wavelength of that tone in air.
- Enter a delay in seconds, such as the gap between lightning and thunder, to see how far the sound traveled in that time.
Formula
c = 331.3 x sqrt(T / 273.15) m/s, with T in kelvin
wavelength = c / frequency
distance = c x time
The result is for dry air treated as an ideal gas. The same speed follows from sqrt(gamma x R x T / M) with gamma 1.4, R 8.314462618 J/(mol K) and M 0.0289647 kg/mol, which agrees to within about 0.01 percent.
A mild day and a thunderstorm
At 20 degrees Celsius (293.15 K) the speed of sound is 331.3 x sqrt(293.15 / 273.15) = 343.21 m/s. That is 1235.6 km/h, 767.7 mph and 1126.0 ft/s. At 0 degrees Celsius it is 331.3 m/s, and at 70 degrees Fahrenheit it is 343.86 m/s.
If thunder arrives 3 seconds after a flash, the sound has traveled 1029.6 m at 20 degrees Celsius, about 0.64 miles. Light arrives almost instantly, so this is a reasonable estimate of how far away the lightning struck. For an echo, half the distance is the distance to the wall.
Why temperature changes the speed
Sound is a pressure wave passed from molecule to molecule. In warmer air the molecules move faster, so they pass the disturbance along faster. Each degree Celsius adds about 0.6 m/s near room temperature. Pressure alone does not change the speed, since the air gets denser and stiffer in the same proportion.
What the number is used for
Audio engineers use the speed of sound to set delays between speakers, acousticians use it to work out room modes, and the formula gives the Mach number of an aircraft once its airspeed is known. Pair it with the Doppler Effect Calculator to find pitch shifts from moving sources and with the Sabine Reverberation Time Calculator for room sound.
More waves and light tools
For related tools on sound and light, try the Sabine Reverberation Time Calculator, Thin Lens Calculator and Telescope Magnification Calculator.
Assumptions and limits
- The air is dry and behaves as an ideal gas.
- The temperature is the same along the whole path of the sound.
- There is no wind. A wind along the path adds to or subtracts from the speed.
- The formula does not apply to water, solids or very thin or very dense gases.
- The temperature in the form is an example. Use the air temperature where you are.
Frequently asked questions
Does humidity matter?
Slightly. Moist air is a little lighter, so sound is a little faster, by well under one percent at ordinary temperatures. The dry air formula is close enough for most uses.
Why does the page accept kelvin?
Many science problems give the temperature in kelvin, and the formula needs kelvin inside. Entering it directly saves a step and avoids a conversion mistake.
How accurate is the thunder distance rule?
The delay times the speed of sound gives the distance to the strike. It is good to a few percent when you time the delay well, but thunder from a long bolt can arrive spread out over several seconds.
What is the speed of sound in water?
It is far higher, near 1480 m/s in fresh water, but this tool covers air only, so do not use its formula for liquids.