The Speed of Sound in Air, Water and Steel — and What Temperature Does To It

Sound has no single speed. It has a speed in a medium, and in a gas that speed climbs with temperature — about 0.6 m/s for every degree, which is the part almost everybody leaves out. This gives the speed in dry air at your temperature from the exact SI gas constant, the same for helium, the tabulated figures for water and steel, and the travel time over a distance you choose, so you can check a thunderclap or an echo.

Last updated 11 Nov 2026

Speed of sound by medium and temperature

Five media, one temperature, travel time included

Medium the sound travels throughThe two gases are calculated from v = √(γRT/M) with the exact SI molar gas constant, so they move when you change the temperature. The three condensed media are tabulated figures that this batch could not source to a standards publication and they do not move with temperature on this page — in reality water’s sound speed rises by roughly 3 m/s per degree near room temperature, which is five times air’s rate, and steel’s falls very slightly. Choosing one of those three makes the temperature field do nothing to the headline, and the page says so where it matters. Helium is here because it is the famous one: it does not raise the pitch of your voice, it raises the resonant frequencies of the cavity your voice resonates in, because the speed of sound in it is almost three times air’s.

Temperature of the gasIn degrees Celsius. Used only for the two gases. The formula underneath needs kelvin, so the page adds 273.15 for you — and that addition is the single commonest arithmetic slip in this topic, because √T with T in Celsius is meaningless and goes imaginary below zero. Note what the square root does to the sensitivity: the speed changes by v/2T per kelvin, which is 0.606 m/s per degree at the freezing point and 0.585 at 20 °C. That is where the famous “331.3 + 0.6 θ” rule comes from, and also why it drifts slowly wrong as you heat the air.

Distance for the travel-time rowsDoes not affect the headline speed at all; it drives the travel-time and echo rows below, which are the reason anybody measures the speed of sound at school. 1000 m is the default because of the thunder rule: light arrives effectively instantly, so the seconds you count between the flash and the bang, multiplied by the speed below, is the distance to the lightning. Three seconds is almost exactly a kilometre in air at 20 °C, which is the version of the rule worth remembering.

The five media side by side, drawn to the numbers above. Bar lengths go as the square root of the speed, so steel fits beside air without flattening it. The shaded row is the medium you chose, the red dot sits at the end of its bar, and the dashed red line carries that speed across the others so you can see the ratio. The air and helium bars are drawn at YOUR temperature, so they both creep rightwards as you warm the gas even while you have water or steel selected.

343.24m/sExample

Dry air at 20 °C, with 1000 m as the distance for the timing rows

One formula for gases, one for everything else, and a rule of thumb that is a tangent

gases: v = √(γRT/M) = √(γP/ρ) · air, to a good approximation: v ≈ 331.3 + 0.606 θ · condensed matter: v = √(K/ρ) · dv/dT = v/2T

γ: the ratio of principal specific heats, and the whole of Laplace’s correction. Newton assumed the compressions were isothermal and got √(P/ρ) = 280 m/s, about 16% too low; the compressions are in fact too fast for heat to leak away, so they are adiabatic, and the factor γ appears. 7/5 = 1.4 for a diatomic gas such as air, 5/3 ≈ 1.667 for a monatomic gas such as helium
R and M: the molar gas constant, which the 2019 SI makes exact at 8.314 462 618 153 24 J mol⁻¹ K⁻¹, and the molar mass in kilograms per mole. Air is 28.9645 g/mol, so 0.028 964 5 kg/mol, and that factor of a thousand is the second commonest slip here after the kelvin
T: absolute temperature, in kelvin. T = θ + 273.15. Nothing about this formula works in Celsius
P and ρ: pressure and density. They appear as a ratio, and for an ideal gas P/ρ = RT/M, so the pressure cancels out entirely: the speed of sound in air does not depend on how much air there is, only on how hot it is and what it is made of
K: the bulk modulus, for a liquid or a solid. This page does not compute from K; it carries tabulated speeds for water and steel, and says so. Water’s K is about 2.2 GPa, steel’s about 160 GPa
0.606: not a fudge. Differentiate √(γRT/M) and you get dv/dT = v/2T; at the freezing point that is 331.32/546.3 = 0.6065 m/s per kelvin. The linear rule is the tangent to the square root at 0 °C, which is why it is good near freezing and 0.18 m/s high at 20 °C

Worked example

Dry air at 20 °C, with 1000 m as the distance for the timing rows
KELVIN FIRST, BEFORE ANYTHING ELSE. T = 20 + 273.15 = 293.15 K. Write it down as its own line. Every wrong answer to this question that is wrong by a factor of about three and a half is this step missing.
ASSEMBLE THE CONSTANT. γR/M = 1.4 × 8.314 462 6 / 0.028 964 5 = 11.640 25 / 0.028 964 5 = 401.880 kg⁻¹ — and √401.880 = 20.0469, which is exactly the coefficient NPL quotes as 20.047. Getting that number out of the constants is a good sign you have the units right.
MULTIPLY BY THE ROOT OF THE TEMPERATURE. v = 20.0469 × √293.15 = 20.0469 × 17.1216 = 343.24 m/s. To three figures, 343 m/s, which is the figure NPL gives for 20 °C.
CHECK IT AGAINST THE RULE OF THUMB. 331.3 + 0.606 × 20 = 331.3 + 12.12 = 343.42 m/s. That is 0.18 m/s high — five parts in ten thousand. For any school purpose the two agree; for a time-of-flight experiment over 10 m they differ by 15 microseconds, which no stopwatch can see.
NOW THE TIMING. Over 1000 m the sound takes 1000 / 343.24 = 2.9134 s, and an echo off a cliff 1000 m away comes back in 5.8269 s. Turn it round: three seconds of sound travels 3 × 343.24 = 1029.7 m. That is the thunder rule, and the error in treating it as exactly one kilometre is 3%.
AND THE SENSITIVITY, WHICH IS THE MARK-WINNING LINE. dv/dT = v/2T = 343.24 / 586.3 = 0.5854 m/s per kelvin. So being 5 °C out about the air temperature costs you 2.9 m/s, or 0.85%. In a resonance-tube experiment that is the same size as the error from ignoring the end correction, which is worth knowing before you blame your tuning fork.

Dry air, computed from the exact SI gas constant, against the linear rule

The linear rule is a **tangent at the freezing point**, not an average fit, and the table shows it: the difference is almost exactly zero at 0 °C and grows in both directions, upward on both sides because the square root is concave. Over the whole range a school ever meets, the rule is good to better than two parts in a thousand, which is why it survives. The last column is the useful one for an experiment: at room temperature the speed moves by 0.59 m/s per degree, so quoting the speed of sound to four figures without quoting the temperature to within a degree is a false precision. The 0 °C row is not quite zero because 331.3 is itself a rounded version of 331.32.
Temperature	v = √(γRT/M), m/s	331.3 + 0.606 θ, m/s	Difference	dv/dT = v/2T
−40 °C	306.10	307.06	+0.96	0.657
−20 °C	319.09	319.18	+0.09	0.630
0 °C	331.32	331.30	−0.02	0.606
20 °C	343.24	343.42	+0.18	0.585
30 °C	349.04	349.48	+0.44	0.576
60 °C	365.90	367.66	+1.76	0.549

The five media on this page, and why they are so different

Read the second column and the third together. Helium beats air not because it is “lighter” in any loose sense but because √(γ/M) is 2.93 times larger: a factor 1.09 from the monatomic γ and a factor 2.69 from the molar mass. Water beats air by a factor of four despite being 800 times denser, because stiffness enters as a square root on top. Steel beats water by four again for the same reason. **Only the top two rows move when you change the temperature field**, and only the top two are derived rather than copied — the three tabulated rows are reproduced from the sibling wave-speed record on this site so the two pages agree, and neither page can cite a standards publication for them.
Medium	Speed, m/s	× air at 20 °C	Where the number comes from
Dry air, 20 °C	343.24	1.00	computed, γ = 7/5, M = 28.9645 g/mol
Helium, 20 °C	1007.43	2.93	computed, γ = 5/3, M = 4.0026 g/mol
Fresh water, 20 °C	1482	4.32	tabulated; no primary source read
Sea water, nominal	1500	4.37	tabulated nominal; varies 1450–1550
Steel, longitudinal	5960	17.36	tabulated; alloy- and mode-dependent

Why there is no such thing as “the” speed of sound

Ask what the speed of sound is and the honest answer is a question back: in what, and at what temperature. The number 343 m/s that everybody remembers is dry air at 20 °C and nothing else. Put the same sound in water and it goes four times faster; put it in a steel rail and it goes seventeen times faster; cool the air to a January morning at −5 °C and it slows to 328 m/s. The medium sets the speed, the source does not. A whistle and a drum travel at the same speed through the same air, which is why an orchestra stays together.

Where the formula comes from, in one paragraph. A sound wave is a travelling squeeze. How fast a squeeze propagates depends on two things: how hard the material pushes back when you compress it, and how much inertia it has. Stiffness over density, square-rooted: v = √(K/ρ). For a gas the stiffness is the pressure itself, but there is a subtlety, and it is the subtlety that makes this a physics question rather than an arithmetic one. Newton assumed the compressions happen slowly enough for the temperature to even out, and predicted √(P/ρ) — about 280 m/s for air, which is 18% too slow, a discrepancy that stood for a century. Laplace saw that at audio frequencies the squeezes are far too fast for heat to flow: they are adiabatic, not isothermal, so the stiffness is γP rather than P. The 1.4 fixes the discrepancy exactly.

Pressure cancels, and that matters. Substituting the ideal gas law into √(γP/ρ) gives √(γRT/M), in which no pressure appears. So the speed of sound at the summit of Everest is not lower because the air is thin — it is lower because the air is cold. At the same temperature, thin air and thick air carry sound at the same speed. Students find this hard to believe and it is worth a moment: halving the pressure halves the stiffness and halves the density, and the ratio is untouched.

What temperature does, and the 0.6 rule. Because v goes as √T, the sensitivity is dv/dT = v/2T — about 0.61 m/s per kelvin at freezing, falling to 0.59 at 20 °C and 0.55 at 60 °C. The rule of thumb v ≈ 331.3 + 0.606 θ is just the tangent to the square root at 0 °C, which is why its coefficient is exactly that freezing-point sensitivity and why it reads a little high everywhere else. Over the range a school meets it is good to two parts in a thousand. Quote the speed of sound to four figures and you have implicitly quoted the temperature to a tenth of a degree, so most four-figure answers in exercise books are honest about the arithmetic and dishonest about the physics.

Liquids and solids, and why they are not on the same footing here. The two gas rows on this page are calculated. The water, sea-water and steel rows are tabulated numbers that this batch could not trace to a standards publication, and they are flagged as such in the references rather than dressed up. Sea water is the softest of the three: its speed genuinely runs from about 1450 to 1550 m/s depending on temperature, salinity and depth, and 1500 is a convention. Steel is worse than it looks, because a solid carries a longitudinal wave and a shear wave at different speeds, and a thin bar carries a third, slower one again; 5960 m/s is the bulk longitudinal figure. If a question gives you a speed for a solid, use the one it gives.

The three places this goes wrong in an exam. Celsius left in the square root; grams per mole left in the denominator instead of kilograms; and γ = 1.4 used for a monatomic gas. The third is the sneakiest, because 1.4 is right so often that it stops looking like a choice. Helium, neon and argon are monatomic and take 5/3. For the companion pages, wave speed, frequency and wavelength turns this speed into a wavelength, and standing waves in pipes is where a resonance-tube experiment gets you this number back out of a ruler and a tuning fork.

Frequently asked questions

Why does sound travel faster in water than in air if water is so much denser?

Because stiffness wins. The speed is √(K/ρ), so density is in the denominator and does slow the wave down — but water is about 800 times denser than air and roughly 15 000 times harder to compress, and √(15 000/800) ≈ 4.3. That is the factor you actually observe. The intuition that dense means slow is only right when you hold stiffness constant, which nature almost never does: dense materials are usually stiff ones.

Does the speed of sound depend on the loudness or the pitch?

To the accuracy of this page, no. Loudness and pitch are properties of the wave; the speed is a property of the medium. That is why music arrives in tune and in time from across a hall. There are second-order effects — a genuinely violent compression such as a shock front from an explosion does travel faster than sound, and very high ultrasonic frequencies disperse slightly in some media — but for everything a school question will ask, one medium means one speed.

Why doesn’t air pressure appear in the formula?

It cancels. Start from v = √(γP/ρ) and substitute the ideal gas law in the form P/ρ = RT/M. The pressure disappears and you are left with √(γRT/M). Physically: compressing the gas makes it stiffer and heavier in exactly the same proportion. So a weather high and a weather low do not change the speed of sound, but the temperature change that comes with them does.

Where does “331.3 plus 0.6 times the temperature” come from?

It is the tangent to the square root at 0 °C. Differentiating √(γRT/M) gives dv/dT = v/2T, and at 273.15 K that is 331.32/546.30 = 0.6065 m/s per kelvin. So the rule is not an empirical fit but calculus, and its accuracy is the accuracy of a tangent: perfect at freezing, 0.18 m/s high at 20 °C, 1.8 m/s high at 60 °C. NPL quotes it in exactly this form.

If I count three seconds between the lightning and the thunder, how far away is the storm?

About a kilometre, and the page gives the exact figure for your temperature. Light covers 1 km in 3.3 microseconds, so the flash is effectively instantaneous and the whole delay belongs to the sound. At 20 °C three seconds is 1029.7 m, so “three seconds per kilometre” is 3% out and the error is in your favour: the storm is slightly further away than the rule says. On a cold night at −10 °C three seconds is only 981 m.

Does helium really make your voice higher?

Not in the way the phrase suggests. Your vocal folds vibrate at much the same rate — they are flesh under tension, not air — so the fundamental frequency barely moves. What changes is the resonances of the cavity above them: those depend on the speed of sound in the gas filling it, which in helium is 2.93 times air’s, so every formant shifts up by that factor and the timbre turns cartoonish. The pitch you sing is nearly unchanged; the colour of the sound is transformed.

Related calculators

References

National Physical Laboratory (UK), Speed of Sound measurement resource (PDF read 11 November 2026). NPL gives the room-temperature working formula c ≈ 331.3 + 0.606 θ m/s with θ in °C, the fuller c = √(γRT/M) which it approximates as 20.047 √(θ + 273.15), and the expected value 343 m/s at 20 °C. This page reproduces all three: the square-root form returns 343.236 m/s at 20 °C and the linear form 343.42, and the 0.606 coefficient is shown below to be c₀/2T₀ at the freezing point, 0.6065, which is where it comes from.
The International System of Units (SI), 9th edition, Bureau International des Poids et Mesures, 2019. The metre is fixed by defining the speed of light in vacuum as c = 299 792 458 m/s exactly, and the Boltzmann and Avogadro constants are fixed exactly too, which makes the molar gas constant R = 8.314 462 618 153 24 J mol⁻¹ K⁻¹ exact. Every speed of sound on these pages is derived from that exact R rather than copied out of a table.
NCERT, Physics Textbook for Class XI, Part II, Chapter 14, Waves. The chapter number was checked by an earlier batch in this project against NCERT’s own answers appendix for Part II, which runs Chapters 8 to 14 and puts Waves at 14; older printings numbered it 15 and much of the web still says 15. Cited for the syllabus treatment of the speed of sound in a gas as the Newton formula v = √(P/ρ) with Laplace’s correction supplying γ, giving v = √(γP/ρ) = √(γRT/M). Citing the chapter is not a claim that any board has approved this page.
The non-gas speeds on these pages — fresh water 1482 m/s at 20 °C, sea water 1500 m/s nominal, steel 5960 m/s longitudinal — are the figures in common tabulation and this batch did not reach a primary standards publication for any of them. They are reproduced unchanged from the sibling record on this site so that the two pages cannot disagree. Sea water is the weakest of the three: its sound speed moves with temperature, salinity and depth across roughly 1450 to 1550 m/s, and 1500 is a round nominal rather than a property of anything. Steel depends on the alloy and on whether the wave is a bulk longitudinal wave or a thin-bar wave, which differ by well over 10%. The usual reference for pure water is Marczak’s 1997 fit in the Journal of the Acoustical Society of America, which was not read here. The gas speeds, by contrast, are derived from exact SI constants and are not tabulated values at all.