Speed of Sound Calculator

Background.

This calculator computes the speed of sound from first principles using the exact physical relationship c = √(γRT/M), where γ is the ratio of specific heats, R is the universal gas constant, T is absolute temperature, and M is the gas's molar mass — rather than relying solely on the popular but medium-specific shortcut formula c ≈ 331.3 + 0.606·T(°C) that most online calculators use without explanation. NASA's Glenn Research Center states the physical formula directly (with temperature required on an absolute scale) as part of its aeronautics curriculum, precisely because it is the version that actually generalizes: it works for any ideal gas, at any reasonable temperature, once you know that gas's γ and M, whereas the linear shortcut only works for air, and only near room temperature.

This page derives the familiar 331.3 and 0.606 constants directly from the physical formula rather than treating them as a separately memorized rule. Evaluating c = √(γRT/M) for dry air at exactly 0°C (273.15 K) using NIST's and NASA's reference values for R, γ, and M produces 331.315 m/s — matching the textbook constant to four significant figures — and taking the first-order Taylor expansion of the same formula around 0°C produces a slope of 0.6065 K⁻¹, matching the textbook 0.606 coefficient just as closely. In other words, both magic numbers in the popular shortcut are simply the exact physical formula, evaluated and linearized at a single reference temperature — not an independent empirical fit requiring its own citation.

Because the physical formula is fully general, this calculator also supports helium as a second medium, letting you see directly why inhaling helium famously (if inadvisably) raises the pitch of a person's voice: helium's much lower molar mass (about 4.0 g/mol, versus roughly 29.0 g/mol for air) makes sound travel through it nearly three times faster than through air at the same temperature, which shifts the resonant frequencies of the vocal tract upward. The calculator reports results in meters per second, kilometers per hour, and miles per hour, and — for air specifically — also reports the classic linear-approximation value alongside the exact physical result, so you can see directly how closely (or not) the shortcut tracks the true value at temperatures away from the 0°C reference point the shortcut is built around.

Speed of sound calculations show up constantly in aviation (Mach number is defined as an aircraft's speed divided by the local speed of sound, which itself changes with altitude because temperature changes with altitude), acoustics and audio engineering, meteorology, and basic physics education. Because the speed of sound in an ideal gas depends on the square root of absolute temperature and does not depend on pressure at fixed composition, the same air at sea level and at 10,000 meters altitude has a meaningfully different speed of sound purely because of the temperature difference between those altitudes — a fact that matters directly for high-altitude aircraft performance calculations.

What is speed of sound calculator?

Sound is a longitudinal pressure wave — a traveling pattern of compressions and rarefactions — that propagates through a medium because molecules collide with and push on their neighbors. The speed at which that disturbance propagates depends on how quickly the medium can transmit those molecular collisions, which for an ideal gas turns out to depend on the gas's temperature, its molar mass, and its ratio of specific heats (γ = c_p/c_v), but not on the pressure at fixed temperature and composition, since higher pressure increases both the restoring force and the inertia of the compressed gas in exactly offsetting proportions.

Lighter molecules move faster on average at a given temperature (kinetic theory ties average molecular speed to temperature and inversely to the square root of molecular mass), and it is that faster molecular motion that lets a pressure disturbance propagate more quickly — which is precisely why the c = √(γRT/M) formula has M in the denominator: lower molar mass produces a higher speed of sound, all else equal. Temperature enters because higher temperature means faster molecular motion (again from kinetic theory), and γ enters because it captures how efficiently compressional energy converts into the pressure-restoring force that drives the wave forward, which differs between monatomic gases like helium (γ = 5/3) and diatomic gases like the nitrogen and oxygen that make up most of air (γ = 7/5 = 1.4).

How to use this calculator.

1. 01Enter the ambient temperature in °C.
2. 02Choose the medium — air or helium.
3. 03Read the exact speed of sound in m/s, km/h, and mph.
4. 04For air, compare against the classic linear-approximation figure to see how well the shortcut tracks the exact physical result at your chosen temperature.

The formula.

For an ideal gas, the exact speed of sound is c = √(γRT/M), where absolute temperature T must be in Kelvin (T = °C + 273.15), R is the universal gas constant (8.314462618 J/(mol·K), an exact CODATA value), γ is the ratio of specific heats (1.4 for the diatomic gases that dominate air; 5/3 ≈ 1.6667 for monatomic helium), and M is the gas's molar mass in kg/mol (about 0.02896546 kg/mol for dry air; 0.004002602 kg/mol for helium). Plugging in higher temperature increases c (through the square-root-of-T dependence, since warmer molecules move faster and transmit pressure disturbances more quickly); plugging in a lower molar mass also increases c, which is the physical reason sound travels faster through helium than through air at the same temperature.

The familiar linear approximation, c(T) ≈ 331.3 + 0.606·T(°C), is not treated on this page as an independently sourced empirical rule — it is derived as the first-order Taylor expansion of the physical formula around a 0°C reference point. Writing T(K) = 273.15 + T(°C) and factoring, c(T) = c₀·√(1 + T(°C)/273.15), where c₀ = c(0°C). For small T(°C)/273.15, the square root is well approximated by its linear term, giving c(T) ≈ c₀·(1 + T(°C)/(2×273.15)) = c₀ + [c₀/(2×273.15)]·T(°C). Evaluating c₀ from the exact air formula gives 331.315 m/s, and the resulting slope works out to 0.6065 — both matching the textbook shortcut's constants to four significant figures, confirming the shortcut is simply this calculator's exact formula, linearized. Because the linearization was built specifically around air's γ and M, it should not be applied to helium or any other gas.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NASA Glenn Research Center. "Speed of Sound." a = √(γRT); temperature must be specified on an absolute scale (Kelvin or Rankine).
2. [2]NASA Glenn Research Center. "Specific Heats — cp and cv." γ = 1.4 for air under standard-day conditions.
3. [3]National Institute of Standards and Technology. CODATA recommended value: molar gas constant R = 8.314462618 J/(mol·K), exact.
4. [4]National Institute of Standards and Technology. "Revised formula for the density of moist air (CIPM-2007)." Molar mass of dry air, 28.96546×10⁻³ kg/mol.
5. [5]National Institute of Standards and Technology. "Atomic Weights and Isotopic Compositions for Helium." Standard atomic weight 4.002602.