Speed of sound calculator

How fast is sound in air?

About 343 m/s (1,126 ft/s, 768 mph) in dry air at 20 °C (68 °F), and about 331 m/s at 0 °C.

How does temperature change it?

The speed grows with the square root of the absolute temperature: v = √(γRT ÷ M). At 30 °C it is about 349 m/s; at −10 °C about 325 m/s.

How can I tell how far away lightning is?

Sound covers a mile in about 4.7 seconds and a kilometer in about 2.9 seconds at 20 °C. Count the seconds from flash to thunder and divide.

Does humidity or pressure matter?

Pressure alone barely changes it. Humidity raises it slightly; this calculator uses dry air.

What values does the calculator use?

γ = 1.4 for air, R = 8.314 J/(mol·K) (OpenStax rounds it to 8.31) and M = 0.02897 kg/mol, as in the OpenStax derivation of the formula.

How do I find the distance to a wall from an echo?

The sound travels to the wall and back, so the distance is d = v·t ÷ 2. At 20 °C (343.2 m/s) an echo that returns after 0.5 s means a wall 85.8 m (281 ft) away. If you used v·t you would get twice the distance.

How fast does sound travel in water or steel?

Much faster than in air. OpenStax University Physics (Volume 1, section 17.2) lists 1,480 m/s for fresh water and 1,540 m/s for sea water at 20 °C, 5,120 m/s in aluminum and 5,960 m/s in steel, against 331 m/s in air at 0 °C. This calculator is only for air; enter such a speed as the wave speed in the wavelength calculator.

The formula and what it assumes

For an ideal gas the speed of sound is v = √(γRT ÷ M), with T the absolute temperature in kelvins, R the gas constant, M the molar mass and γ the ratio of specific heats (OpenStax University Physics, Volume 1, section 17.2, Eq. 17.6). For air OpenStax uses γ = 1.40 and M = 0.02897 kg/mol, which is the same as v = 331 m/s × √(T ÷ 273 K) (Eq. 17.7). The speed depends on the temperature, not on the pressure, and is almost independent of frequency. The calculator uses dry air and converts °F to kelvins with K = (°F − 32) × 5/9 + 273.15. The exact gas constant is 8.314462… J/(mol·K); OpenStax rounds it to 8.31.

Worked example: air at 77 °F

77 °F is (77 − 32) × 5/9 = 25 °C, or 298.15 K. Then v = √(1.4 × 8.314 × 298.15 ÷ 0.02897) = 346.1 m/s, which is 1,136 ft/s or 774 mph. Compare 20 °C (343.2 m/s) and 0 °C (331.3 m/s): every extra degree adds about 0.6 m/s near room temperature. OpenStax Example 17.1 gives 348.7 m/s at 30 °C with the rounded 331 m/s formula; this calculator gives 349.0 m/s.

Common mistakes

Putting °C or °F into the formula instead of kelvins is the first one; the temperature must be absolute. The second is treating 343 m/s as a constant. It holds at 20 °C only: at −10 °C sound travels at 325 m/s, about 5% slower. The third is using the air value for another medium, as the FAQ above shows. And remember that the speed of sound is a property of the air, not of the source: a moving source changes the pitch you hear (the Doppler calculator covers that), not the speed of the sound.

Sources: OpenStax University Physics, Volume 1, section 17.2 (speed of sound, Eq. 17.6–17.7; Example 17.1; table of speeds in media); the gas constant is the exact SI value (CODATA, NIST) and the foot and mile-per-hour factors are from NIST SP 811, Appendix B.8. Related: wavelength calculator, Doppler effect calculator, standing wave calculator and free fall calculator.