How this instrument works
Sound is a pressure disturbance handed from one air molecule to the next, so its pace is capped by how briskly those molecules are already jostling. Temperature is precisely a measure of that agitation, which is why a single variable governs the whole business. Warm that air and collisions arrive sooner, each nudge is relayed faster, and the square root is honest accounting: mean molecular speed scales with √T, so sound does too. Note what this expression counts from — 273.15, not zero — because only absolute temperature carries that meaning.
The 331.3 is a measurement rather than a derivation: speed through dry air at exactly freezing point, pinned down by three centuries of stubborn fieldwork. William Derham, a rector in Essex, spent 1709 watching distant cannon flashes through a telescope from his church tower and timing each report against a half-second pendulum. He reported roughly 1,072 feet per second and, more usefully, established that wind shifted his answer while loudness and pitch did not. The Paris Academy settled it in 1738 by firing cannon between Montmartre and Montlhéry, some 29 km apart, in both directions on one night so that any breeze would cancel; their figure, reduced to 0 °C, sits within a couple of metres per second of what this sheet uses.
What this formula assumes is dry air behaving as an ideal gas at ordinary densities. Notice what is absent: pressure. Stiffness springs a wave forward and density holds it back, both scale with pressure, and so pressure cancels out of the algebra completely — a barometer tells you nothing here. Humidity is a genuine correction but a tiny one, and it points opposite to most people's intuition. Push far below −100 °C and the ideal-gas picture frays; ask for −273.15 °C and you get zero back, which is arithmetic rather than prophecy, since air has long since liquefied and left nothing behind to carry a wave.
- Put your reading into Air temperature (°C) — the temperature of the air the sound actually crosses, not the ground and not the forecast high.
- Read Speed of sound in air below. Its unit menu carries m/s as standard, plus ft/s, km/h and mph.
- Audit against three anchors: 331.3 m/s at freezing, 343.2 m/s at 20 °C, and close to 352 m/s on a 35 °C afternoon.
- For a distance, multiply by a delay you timed. For a Mach number, divide true airspeed by whatever figure appears.
- Working aloft, enter the temperature at altitude rather than at the field. Cruise level near −57 °C yields roughly 295 m/s.
Worked example — thunder on a freezing night
A still, clear night with ice setting on the puddles, and a porch thermometer reading exactly 0 °C. Enter 0 into Air temperature (°C); Speed of sound in air returns 331.3 m/s, because that bracket becomes 1 + 0 ⁄ 273.15 = 1, whose square root is 1, leaving the constant to pass through untouched. Flip the units and an identical answer reads 1,192.7 km/h, 741.1 mph, or 1,087 ft/s — that last being the number printed in every imperial-era physics textbook.
Now put it to work. Lightning flares over a far ridge and thunder arrives five seconds behind: 331.3 × 5 = 1,656.5 m, so that strike landed about 1.7 km off. Had an identical storm rolled through on a 20 °C evening, sound would have covered 343.2 × 5 = 1,716 m instead, placing the strike some 60 metres further away. Which is exactly why counting three seconds to the kilometre makes a decent field estimate and a poor instrument — it quietly assumes a temperature nobody bothered to check.
Questions
Does air pressure or altitude change the speed of sound?
Pressure does not, which catches most people out. In an ideal gas the bulk modulus springing a wave forward and the density holding it back are both proportional to pressure, so their ratio survives untouched and pressure drops out of the algebra completely. Sound therefore crosses a mountain summit at the same rate as sea-level air of identical temperature. Altitude does slow it in practice, but only because air up there is colder — an effect the temperature field already accounts for.
Is sound slower through humid air?
Faster, marginally, and the opposite intuition is worth unlearning. Humid air feels heavy yet is physically lighter: a water molecule weighs 18 g/mol against roughly 29 for the nitrogen and oxygen it displaces, so saturated air is less dense than dry air at matching temperature and pressure. Magnitude is small — under 0.4% even at 30 °C and full saturation, worth about 1.3 m/s. This sheet models dry air, so treat its answer as a floor on a muggy day rather than an error.
Why does it return zero at −273.15 °C?
Because that bracket collapses to zero there, and √0 = 0. Read it as a property of the algebra, not a prediction. The expression describes an ideal gas whose molecules relay a disturbance by colliding; absolute zero is where such thermal motion formally ceases, leaving the model nothing to propagate. Real air never arrives — oxygen liquefies near −183 °C and nitrogen near −196 °C — and well before either point the ideal-gas assumption has stopped earning its keep.
Does this formula work for helium, water, or steel?
No. That 331.3 belongs to dry air at 0 °C and carries air's composition and adiabatic index folded inside; change the gas and the constant is simply wrong. Helium at 0 °C runs near 970 m/s because its molar mass is seven times smaller — which is also what makes an inhaled voice odd. Vocal folds keep vibrating at their original frequency; throat resonances shift upward, so timbre changes rather than pitch. Liquids and solids need a different expression entirely, built from bulk modulus and density.
How does Mach 1 depend on this number?
Mach number is true airspeed divided by local sound speed, so Mach 1 names no fixed velocity — it is whatever this sheet returns for whichever air an aircraft happens to occupy. Over a 15 °C sea-level field that means about 340 m/s. At a typical cruise altitude of 11 km, standard-atmosphere temperature sits near −56.5 °C and sound speed falls to roughly 295 m/s. Identical true airspeed therefore buys a higher Mach number the higher and colder you climb, which is why transonic aircraft are limited by Mach rather than by knots up there.
Is the rule of 0.6 m/s per degree good enough?
Near room temperature, yes. That square root is gentle enough over ordinary weather that a straight line through it stays honest: between 0 °C and 30 °C the linear rule and the true curve differ by under half a metre per second. Stretch further and it drifts. At −40 °C the shortcut predicts about 307 m/s against a true 306.1, and the gap keeps widening. Below freezing or above roughly 40 °C, use the square root and let the arithmetic carry it.