Speed of Sound Calculatorv = √(γRT ÷ M)
The speed of sound in dry air depends on temperature: v = √(γRT ÷ M), about 331.3 m/s at 0 °C and 343 m/s at 20 °C, rising roughly 0.6 m/s per degree. Enter an air temperature, pick a medium such as water or steel, or time an echo to measure a distance. You get the speed in m/s, km/h, mph and knots, plus the Mach 1 figure for that air.
Formula verified against OpenStax — University Physics, Volume 1 · NASA Glenn — Beginner’s Guide to Aeronautics
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Conditions
Calculated for dry air; humidity adds up to about 0.5% at room temperature.
Step-by-step working
What is speed of sound?
The speed of sound is how fast a pressure wave travels through a medium: about 343 m/s in room-temperature air. It depends on the medium’s stiffness and density, and in gases on temperature.
It sets the delay between lightning and thunder, defines Mach 1 for aircraft, lets bats and sonar measure distance with echoes, and determines the wavelengths of musical notes.
Quick answers
How does temperature affect the speed of sound?
Sound speeds up by about 0.6 m/s for every 1 °C rise in air temperature, because warmer molecules move faster. It is 331 m/s at 0 °C and 349 m/s at 30 °C.
What is the speed of sound in mph and km/h?
At 20 °C it is 767 mph or 1,235 km/h. At the standard sea-level temperature of 15 °C it is 761 mph (340.3 m/s).
Why is sound faster in water and steel?
Speed depends on stiffness over density. Water and steel are far stiffer than air relative to their density, so sound travels about 4.3× and 17× faster.
How far away is lightning?
Count the seconds between flash and thunder and multiply by 343 m (or divide by 3 for km). Our science hub has a dedicated lightning distance calculator.
Speed of sound formula
For dry air: γ = 1.4, R = 8.314 J/(mol·K), M = 0.02896 kg/mol. T must be in kelvin.
| Symbol | Meaning | SI unit |
|---|---|---|
| v | Speed of sound | m/s |
| γ | Adiabatic index (heat capacity ratio) | — |
| R | Molar gas constant | J/(mol·K) |
| T | Absolute temperature | K |
| M | Molar mass of the gas | kg/mol |
| t | Echo time (there and back) | s |
How to calculate the speed of sound in air
- Convert the temperature to kelvin: add 273.15 to °C.
- Multiply γ × R × T and divide by M.
- Take the square root to get m/s.
- Quick check: 331 + 0.6 × T(°C) is accurate to within about 0.5 m/s near room temperature.
Worked example: sound on a 20 °C day
How fast does sound travel in dry air at 20 °C?
v = √(1.4 × 8.3145 × 293.15 ÷ 0.028964) = 343.2 m/s
= 1,235.6 km/h = 767.8 mph
A shout that echoes back from a cliff after 1.5 s means the cliff is 343.2 × 1.5 ÷ 2 ≈ 257 m away.
Speed of sound in different media
Approximate values for longitudinal (pressure) waves.
| Medium | Speed (m/s) | vs air |
|---|---|---|
| Air, 0 °C | 331 | 0.96× |
| Air, 20 °C | 343 | 1× |
| Helium | 1,007 | 2.9× |
| Water, 20 °C | 1,481 | 4.3× |
| Seawater | ≈ 1,500–1,530 | ≈ 4.4× |
| Ice | 3,880 | 11× |
| Steel | 5,960 | 17× |
| Diamond | 12,000 | 35× |
Common mistakes to avoid
- Using °C in the formula. T must be absolute (K), or the square root makes no sense below 0 °C.
- Forgetting to halve echo distances. The sound goes there and back.
- Assuming pressure changes the speed in air. At a given temperature, an ideal gas’s sound speed doesn’t depend on pressure.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Speed of Sound Calculator: frequently asked questions
About 343 m/s (1,235 km/h, 767 mph) in dry air at 20 °C. It varies with temperature and medium.
Hot air. The speed is proportional to the square root of absolute temperature.
No. Sound is a mechanical wave and needs a medium of particles to pass along the vibration.
The local speed of sound. At sea level and 15 °C it is about 340 m/s; at 11 km altitude (−56.5 °C) it drops to about 295 m/s.
Slightly. Humid air is less dense, so sound travels up to about 0.5% faster at room temperature.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 17.2, Speed of Sound
- NASA Glenn — Beginner’s Guide to Aeronautics — Speed of Sound and Mach number
- NIST — CODATA 2022 Fundamental Physical Constants — molar gas constant R
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.