Speed of Sound in Air Calculator
Enter air temperature, humidity and atmospheric pressure to instantly find how fast sound travels in air. Results are given in m/s, km/h, ft/s, mph and knots, with the humidity effect and reference values.
How Fast Does Sound Travel at Your Temperature?
Speed of Sound in Air Formula
Where:
- \(c\) — speed of sound in air (m/s)
- \(\gamma = 1.4\) — ratio of specific heats for air (a diatomic gas)
- \(R = 8.31446\ \text{J/(mol·K)}\) — universal gas constant
- \(T\) — absolute temperature of the air (K)
- \(M\) — molar mass of the air (kg/mol): 0.0289644 for dry air, lower for humid air
For humid air, the molar mass is obtained from the dry-air and water-vapour partial pressures: \( M = \dfrac{p_d M_{dry} + p_v M_{vap}}{p} \), where the water-vapour partial pressure \(p_v\) follows the Magnus saturation-vapour-pressure formula. This is the ideal-gas expression for the adiabatic speed of sound — the key point being that sound speed depends on temperature and gas composition, not on air pressure itself.
Speed of Sound in Air – Calculation Example
Example: air at 20 °C, 50 % relative humidity and standard pressure of 1013.25 hPa (the calculator's default values).
\[ T = 20 + 273.15 = 293.15\ \text{K} \]
\[ p_v = 0.50 \times 6.112\, e^{\frac{17.62 \times 20}{243.12 + 20}} \approx 11.66\ \text{hPa} \]
\[ M = \frac{1001.59 \times 0.0289644 + 11.66 \times 0.0180153}{1013.25} \approx 0.028840\ \text{kg/mol} \]
\[ c = \sqrt{\frac{1.4 \times 8.31446 \times 293.15}{0.028840}} \approx 343.97\ \text{m/s} \]
Result: the speed of sound is about 343.97 m/s (1238.3 km/h, 1128.6 ft/s, 769.4 mph, 668.6 kn). Dry air at the same temperature gives 343.24 m/s, so humidity adds about 0.73 m/s.
How to use the calculator
- Enter the Air temperature (T) and choose its Unit — °C, °F or K. The value is converted internally to kelvin.
- Optionally enter the Relative humidity (RH) as a percentage between 0 and 100. Leave the field blank if you want dry air.
- Enter the Atmospheric pressure (p) and select its Unit (hPa, kPa, inHg, mmHg or atm). Standard sea-level pressure, 1013.25 hPa, is pre-filled.
- Read the Estimated speed of sound (c) in metres per second, along with conversions to km/h, ft/s, mph and knots.
- Check the Details block for the absolute temperature, the dry-air speed, the humidity effect, the vapour pressure and the molar mass used in the calculation.
What is the speed of sound in air?
Sound is a pressure wave that travels through air by compressing and expanding it. Because these compressions happen so quickly, no significant heat escapes, and the wave propagates adiabatically — which is why the ratio of specific heats \(\gamma\) appears in the formula. In dry air at 0 °C the speed of sound is 331.3 m/s; at a comfortable room temperature of 20 °C it rises to about 343 m/s, roughly 1235 km/h.
Temperature is by far the dominant factor. Hotter air means faster-moving molecules, which pass pressure disturbances along more quickly: the speed scales with the square root of the absolute temperature, so it rises by roughly 0.6 m/s per degree Celsius near room temperature. A handy approximation for dry air is \( c \approx 331.3 + 0.606\,T(°C) \) m/s.
Humidity has a smaller but measurable effect, and it works in a direction many people find counter-intuitive: humid air is less dense, because water-vapour molecules (18.02 g/mol) are lighter than the nitrogen and oxygen they displace (28.96 g/mol average). Lighter molecules move faster at the same temperature, so sound travels slightly faster in moist air — typically 0.5 to 1 m/s faster at room temperature and moderate humidity. Atmospheric pressure itself has almost no influence: at a fixed temperature, denser air also has proportionally higher pressure, and the two effects cancel, leaving pressure to matter only through the small humidity correction.
The speed of sound matters in many practical situations: estimating the distance to a lightning strike (count the seconds until thunder and multiply by ~343 m/s), room and concert-hall acoustics, echo and sonar timing, and defining Mach numbers in aerodynamics. It also underpins the Doppler effect, since the pitch shift of a passing siren depends on how the source speed compares with the sound speed.
Reference values
| Air temperature | Speed of sound (dry air) |
|---|---|
| −40 °C | 306.0 m/s |
| 0 °C | 331.3 m/s |
| 10 °C | 337.4 m/s |
| 20 °C | 343.2 m/s |
| 40 °C | 354.7 m/s |
| 60 °C | 365.9 m/s |
Assumptions and limitations
- The calculation treats air as an ideal gas with a constant \(\gamma = 1.4\), which is accurate to within a fraction of a percent for everyday temperatures (roughly −50 °C to +60 °C). At very high or very low temperatures the result becomes an approximation.
- The result applies to still air. Wind does not change how fast sound moves relative to the air, but it changes the speed relative to the ground — a tailwind carries sound further, a headwind shortens its reach.
- High-frequency sound (ultrasound) and very loud shocks (blast waves, sonic booms) travel faster than the small-amplitude value computed here, because they are not perfectly linear adiabatic waves.
- Humidity is handled with the Magnus formula (CIPM-81/89 approach), which is very accurate between about −45 °C and +60 °C; outside this range the vapour-pressure estimate, and hence the humidity correction, degrades.
- Variations in CO₂ concentration or altitude-related composition changes shift the molar mass slightly; for ordinary air the effect is well below 1 m/s.
Practical tips
For most quick estimates, temperature alone is enough — you can leave the humidity field blank and ignore pressure, since their combined effect rarely exceeds 1 m/s. If you are timing echoes or measuring distances with sound (for example, timing a clap reflected off a wall), divide the round trip by two before comparing with the speed. To convert a distance into a sound travel time, or to work with waves in general, the Wave Speed and Average Speed calculators can help with the follow-up calculations.
Frequently Asked Questions
How do I calculate the speed of sound by hand?
Convert the temperature to kelvin (\(T(°C) + 273.15")), then apply \(c = \sqrt{\gamma R T / M}\) with \(\gamma = 1.4\), \(R = 8.31446\ \text{J/(mol·K)}\) and \(M = 0.0289644\ \text{kg/mol}\) for dry air. At 20 °C this gives \(\sqrt{1.4 \times 8.31446 \times 293.15 / 0.0289644} \approx 343.2\) m/s. For a quick estimate without a calculator, use the rule of thumb \(c \approx 331.3 + 0.606\,T(°C)\) m/s.
Why doesn't atmospheric pressure change the speed of sound?
At a fixed temperature, the ideal-gas formula contains no pressure term for dry air: if you compress the air, its density and pressure rise in the same proportion, and the two effects cancel exactly. This surprises many people, who assume denser air means faster or slower sound. Pressure only enters the calculation indirectly, through the small humidity correction, because it determines how much water vapour the air can hold at a given relative humidity.
Does sound travel faster in humid or dry air?
Faster in humid air, though only slightly — typically 0.5 to 1 m/s at room temperature. Water-vapour molecules (18.02 g/mol) are lighter than the nitrogen–oxygen mixture they replace (28.96 g/mol average), and lighter molecules move faster at the same temperature, so pressure disturbances travel quicker. The effect is largest in warm, humid air and negligible below about 30 % relative humidity.
What is the speed of sound at different temperatures and altitudes?
In dry air: about 331.3 m/s at 0 °C, 343.2 m/s at 20 °C, 354.7 m/s at 40 °C and 306 m/s at −40 °C. Altitude itself doesn't matter — only the temperature does. Airliners cruise around −55 °C, where sound travels near 296 m/s, while a hot desert afternoon at 45 °C pushes it above 358 m/s. That's why the calculator only needs temperature plus, optionally, humidity and pressure.
How can I use the speed of sound to estimate the distance to lightning?
Start counting seconds the moment you see the flash and stop when you hear thunder, then multiply the count by 343 m/s (about 1 km every 3 seconds, or 1 mile every 5 seconds at 20 °C). Because the temperature may differ, divide the seconds by 2.9 for km in warm air or 3.1 in cold air for better accuracy. If the gap is under 10 seconds, the storm is close — seek shelter immediately.
What are the most common mistakes when calculating sound speed?
The biggest error is forgetting to convert Celsius to kelvin — always add 273.15 before using the formula. Others include assuming higher pressure means faster sound, expecting humidity to slow sound down, and confusing the speed of sound with the speed of light when timing events. Also remember this result is for still air relative to the air itself; wind adds to or subtracts from the ground-relative speed, and shock waves travel faster than this small-amplitude value.
How is Mach number related to the speed of sound?
Mach number is an object's speed divided by the local speed of sound: \(Ma = v / c\). Because \(c\) varies with air temperature, an aircraft flying at a constant true airspeed has a different Mach number at different altitudes. At 20 °C, Mach 1 equals about 343 m/s (1236 km/h), while in the −55 °C stratosphere it drops to roughly 296 m/s. Use this calculator to find the correct \(c\) for your conditions before computing Mach.