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Science

Speed of Sound in Air Calculator

Enter the air temperature in °C, °F or K and the tool computes the speed of sound in dry air using v = 331.3 · √(1 + T/273.15) m/s, with parallel readouts in m/s, km/h, mph, ft/s and knots plus the Mach ratio against the ICAO sea-level reference of 340.29 m/s. Punch in the number of seconds between a lightning flash and its thunder and you also get the distance to the storm. Useful for audio / film work, weather watching, drone acoustics, ballistics and jet-aircraft Mach calculations.

Speed of sound v

Other units

metres / second (m/s)
kilometres / hour (km/h)
miles / hour (mph)
feet / second (ft/s)
knots

Lightning distance

Formula

v = 331.3 · √(1 + T / 273.15) m/s (T in °C) Derivation: v = √(γ · R · T_K), with γ = 1.4 for diatomic air and R_specific = 287.058 J·kg⁻¹·K⁻¹

Frequently asked

Why does the speed of sound not change with air pressure?

The ideal-gas relation v = √(γ · R · T_K) contains only absolute temperature and the specific gas constant — pressure is absent. Intuitively, raising pressure increases the density of the air (which would slow sound) but also increases its stiffness by exactly the same factor (which speeds sound up). The two cancel out, leaving temperature as the only knob. Measurements at the bottom of submarines (100× higher pressure) and on top of mountains (half pressure) agree: sound-speed differences trace to temperature, not pressure.

Do humidity and CO₂ content matter?

Tiny in everyday conditions. Saturated humid air (100 % RH) has γ ≈ 1.401 vs 1.400 for dry air, and water-vapour molecules (M = 18 g/mol) are lighter than N₂/O₂ (M ≈ 29 g/mol), so the speed of sound rises by only about 0.3–0.4 %. Doubling CO₂ content lowers it by ≈ 0.03 %. Going below those numbers needs the full moist-air formula (Cramer 1993, used by NIST) for applications like precision acoustics, supersonic wind tunnels and sonar metrology. For everyday work — film/audio, weather, drones, ballistics — the dry-air formula here is plenty accurate.

How do I use the count-the-seconds rule for lightning distance?

Start timing when you see the flash; stop when you hear the thunder. Seconds ÷ 3 ≈ distance in kilometres, seconds ÷ 5 ≈ distance in miles. Light travels essentially instantaneously over weather distances, while thunder travels at the speed of sound (≈ 343 m/s at 20 °C). This calculator uses the actual temperature you enter, so it gives a slightly more accurate result — e.g. ≈ 349 m/s on a 30 °C tropical evening or ≈ 331 m/s on a 0 °C winter night, about ± 3 % from the standard rule. If the delay is under 5 seconds, the strike is less than 2 km away — get indoors immediately.

Why does a jet's Mach number depend on altitude and temperature?

Mach number is aircraft speed ÷ local speed of sound, and the local speed of sound depends on √T_K — it is not a constant. At sea-level ISA (15 °C) it is 340.29 m/s, the ICAO reference. At a typical cruise altitude of 11 km the air is around −56.5 °C and the speed of sound drops to 295 m/s, so the same Mach 0.85 is 1041 km/h at sea level but only 902 km/h up there. A Boeing 747 cruises at Mach 0.85 to stay below the transonic drag rise; the SR-71 reaches Mach 3.2 in the lower stratosphere where thin air keeps drag low but skin temperatures still hit 300 °C+. This calculator quotes Mach relative to the ICAO sea-level reference so values are easy to compare in everyday work.

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