Speed of sound calculator
The speed of sound in dry air, worked from √(γRT/M) rather than from the rule of thumb — with the rule of thumb shown beside it, so you can see where it gives up. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
The rule of thumb is a fit, not an approximation
Everyone learns 331.3 + 0.606t. It is a straight line, and the real relationship is a square root — c = √(γRT/M), where T is absolute temperature. A straight line cannot be a square root, so the two must part company somewhere.
Where they part is the interesting bit. Sweeping from −80 °C to 200 °C, the straight line touches the real curve at exactly two points: −4.82 °C and +5.73 °C. Between those it never departs by as much as 0.02 m/s, which no measurement anybody makes with a stopwatch and a field would resolve.
| Temperature | Real | Rule of thumb | Out by |
|---|---|---|---|
| −40 °C | 306.10 | 307.06 | 0.96 |
| 0 °C | 331.32 | 331.30 | 0.02 |
| 20 °C | 343.23 | 343.42 | 0.19 |
| 100 °C | 387.24 | 391.90 | 4.66 |
The band where the rule is indistinguishable from the physics is exactly the band of ordinary outdoor air — which is the only range anybody ever checks it in. It was fitted there. Testing it at room temperature can only ever confirm it, whatever it is doing everywhere else.
This site has now met that shape three times: an inverted API gravity formula that is right at exactly 10°, a trigonometry identity that survives being tested at sin(0), and this. The memorable value to check is very often the one value that cannot tell you anything.
It does not depend on pressure
Sound travels at the same speed at the top of a mountain as at sea level, at the same temperature. That surprises people, because thinner air feels like it ought to carry sound more slowly.
The reason is in the formula: pressure appears in both the stiffness and the density of the gas, and cancels. What is left is temperature, the gas constant, and what the gas is made of. Altitude changes the speed of sound only through the fact that it is colder up there.
Humid air is faster, not slower
Water vapour has a molar mass of 18 against dry air's 29, so moist air is lighter than dry air at the same pressure. Lighter gas, faster sound. It is a small effect — a fraction of a percent — and this page does not model it, but it goes the opposite way to most people's intuition.