Speed of Sound Calculator

Speed of sound in an ideal gas: c = √(γRT). Covers all common gases with presets for γ and R.

Compressible Flow · Fundamental

Gas presets — click to fill γ and R

Inputs

Specific heat ratio γ (dimensionless)

c_p/c_v — 1.4 for air, 1.667 for monatomic gases

Specific gas constant R (J/(kg·K))

R = R_u/M — 287.05 for air, 2077 for helium

Temperature T (°C)

T = 293.15 K

Theory

Speed of sound in an ideal gas:

c = √(γ × R × T) [m/s]

R = R_u / M [specific gas constant, J/(kg·K)]

Where:

γ = c_p/c_v — ratio of specific heats (dimensionless)
R = specific gas constant [J/(kg·K)] = R_u/M
R_u = 8.314 J/(mol·K) — universal gas constant
M = molar mass of the gas [kg/mol]
T = absolute temperature [K] — must be in Kelvin

Gas properties and speed of sound at 20°C (293.15 K):

Gas	γ	R [J/(kg·K)]	c at 20°C [m/s]
Air (dry)	1.400	287.05	343
Nitrogen N₂	1.400	296.80	349
Oxygen O₂	1.395	259.83	326
Helium	1.667	2077.1	1007
Hydrogen H₂	1.405	4124.2	1270
Argon	1.667	208.13	323
CO₂	1.289	188.92	267
Methane CH₄	1.303	518.28	446

ISA standard atmosphere (air):

Altitude [m]	T [K]	c [m/s]
0 (sea level)	288.15	340.3
1 000	281.65	336.4
5 000	255.65	320.5
10 000	223.25	299.5
20 000	216.65	295.1

The speed of sound increases with temperature because higher T means faster molecular motion. In the ISA atmosphere, c decreases with altitude as temperature drops (lapse rate −6.5 K/km in the troposphere).