Speed of Sound & Lightning Distance Calculator

About the Speed of Sound & Lightning Distance Calculator

How fast sound travels depends on what it travels through. This calculator gives the speed of sound:

• In air, from the temperature, the humidity and the pressure: air as an ideal gas, c = √(γ·R·T ÷ M), with the water vapour mixed in, which makes moist air a little faster. Add a speed to get its Mach number.
• At an altitude of the U.S. Standard Atmosphere, from −1,000 m to 86 km, with the temperature and pressure there and the Mach number of an aircraft.
• In seawater, from its temperature, salinity and depth, with Mackenzie’s nine-term equation.
• In other materials: gases, liquids and solids from OpenStax University Physics, with the time sound takes to cross a distance.
• To lightning: the seconds between the flash and the thunder give the distance, with the National Weather Service’s safety advice.

With a Pro pass, copy the result or download it as a CSV, or unlock this one result. Without a pass the free preview shows the speed of sound or the lightning distance in full, with the first rows of the table and the first step of the working; every other figure is hidden.

Common uses

• Physics homework on the speed of sound in gases, liquids and solids
• Working out the Mach number of an aircraft, a drone or a projectile at its altitude
• Setting the speed of sound for an echo, sonar or ultrasonic distance measurement
• Telling how far away a thunderstorm is from the delay of its thunder
• Seeing how temperature and humidity change the speed of sound for acoustics and audio

The formulas

• An ideal gas: c = √(γ·R·T ÷ M), with T in kelvins, R = 8.314 J/(mol·K), and for dry air γ = 1.4 and M = 28.96 g/mol: 331.3 m/s at 0 °C and 343.2 m/s at 20 °C
• Humid air: the water vapour’s share of the air, x = humidity × saturation vapour pressure ÷ pressure (the WMO formula), lowers the molar mass, M = (1 − x)·28.96 + x·18.015 g/mol, and γ a little, (C_p ÷ R = 3.5 for the air and 4 for the vapour)
• The standard atmosphere: the temperature falls 6.5 °C per km up to 11 km, stays at −56.5 °C to 20 km, then rises again; c = √(1.40 × 8.31432 × T ÷ 0.0289644)
• Seawater (Mackenzie): c = 1448.96 + 4.591T − 0.05304T² + 0.0002374T³ + 1.340(S − 35) + 0.01630D + 1.675·10⁻⁷D² − 0.01025T(S − 35) − 7.139·10⁻¹³TD³, for −2 to 30 °C, salinity 30 to 40 and depths to 8,000 m
• Mach number: M = v ÷ c
• Lightning: distance = c × the delay; about 3 seconds per kilometre, 5 seconds per mile

Why temperature matters most

In a gas, sound is passed on by molecules bumping into each other, so it travels about as fast as they move, which depends on the temperature. For an ideal gas the pressure cancels out of the formula: higher up, the thin air carries sound more slowly only because it is colder. Near room temperature the speed rises by about 0.6 m/s for each degree.

In liquids and solids the molecules are packed close and held by strong forces, so sound is much faster: about 1,480 m/s in fresh water and 5,960 m/s in steel. Soft vulcanized rubber is the exception at 54 m/s.

Lightning safety

From the NOAA National Weather Service:

• When Thunder Roars, Go Indoors! If you hear thunder, you are likely within striking distance of the storm.
• There is no safe place outside when thunderstorms are in the area. Substantial buildings and hard-topped vehicles are safe options; rain shelters, small sheds and open vehicles are not.
• Wait 30 minutes after the last lightning or thunder before going back outside.
• Lightning often strikes more than three miles from the centre of the thunderstorm, and “bolts from the blue” can strike 10–15 miles from it.

The distance tells you where that flash was, not where the next one will be.

Sources

• OpenStax, University Physics Volume 1, §17.2 Speed of Sound: c = √(γ·R·T ÷ M), γ = 1.4 for air, and Table 17.1, the speed of sound in various media (CC BY 4.0)
• OpenStax, University Physics Volume 2, §2.3 Heat Capacity and Equipartition of Energy and §3.5 Heat Capacities of an Ideal Gas: the heat capacities used for humid air (CC BY 4.0)
• WMO-No. 8, Guide to Meteorological Instruments and Methods of Observation, Annex 4.B: the saturation vapour pressure over water
• NIST: the molar gas constant, R = 8.314 462 618 J/(mol·K), exact
• U.S. Standard Atmosphere, NOAA and NASA, report NASA-TM-X-74335: the temperatures, lapse rates and pressures of its layers, and its constants
• K. V. Mackenzie, Nine-term equation for sound speed in the oceans, Journal of the Acoustical Society of America
• NOAA National Weather Service: lightning safety and lightning myths

Limitations

• Air is treated as a mixture of ideal gases; precise acoustic standards add small real-gas and carbon dioxide corrections, so the last digit may differ slightly from theirs.
• The standard atmosphere is an average: real air on any day is warmer or colder, so the speed at an altitude varies with the weather.
• Mackenzie’s equation holds only for −2 to 30 °C, salinities of 30 to 40 and depths to 8,000 m; fresh and brackish water are outside it (see “Other materials” for fresh water).
• The speeds of the materials are typical values: real alloys, glasses and plastics differ, and a thin rod carries sound more slowly than a large block.
• The lightning distance is an estimate for that one flash; it is not a warning system. If you can hear thunder, go indoors.

Privacy

On this device: nothing is sent

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.