The rms velocity relates the temperature of a gas to the kinetic energy of its molecules. It is close to the speed of sound in the gas and is used to explain diffusion and effusion rates (Graham’s law).
How to use the Root Mean Square Velocity Calculator
- Gas
- Molar mass M (g/mol)
- Temperature T
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the gas (or enter its molar mass) and the temperature.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Gas | Choose one: Air, Nitrogen N₂, Oxygen O₂, Hydrogen H₂ … |
| Molar mass M (g/mol) | A number |
| Temperature T | Units: K, °C, °F |
What each result means
- RMS velocity = sqrt(3×8.314462618×[Temperature T]÷([Molar mass]÷1000))
- Mean speed = sqrt(8×8.314462618×[Temperature T]÷(pi×[Molar mass]÷1000))
Example values
How the main result changes when Molar mass M changes and everything else stays at the example values above:
| Molar mass M (g/mol) | RMS velocity (m/s) |
|---|---|
| 14.48 | 506.7087 |
| 21.72 | 506.7087 |
| 28.97 | 506.7087 |
| 36.21 | 506.7087 |
| 43.45 | 506.7087 |
| 57.93 | 506.7087 |
Formula
v_rms = √(3RT/M)Worked example
Inputs — Gas: Air; Temperature T: 298.15 K.
Results — Molar mass = 28.965 g/mol; RMS velocity = 506.7087 m/s; Mean speed = 466.83971 m/s.
Key terms
- RMS speed
- Square root of the mean of squared speeds.
Frequently asked questions
What is the rms speed of air molecules?
About 500 m/s at room temperature.
Why do lighter gases move faster?
At the same kinetic energy, lower mass means higher speed.
What is Graham's law?
Effusion rate is inversely proportional to √M.
Does pressure affect the rms speed?
No – only temperature and molar mass.
What formula does the Root Mean Square Velocity Calculator use?
v_rms = √(3RT/M).