# Root Mean Square Velocity Calculator

URL: https://speedycalculator.com/calculators/physics/root-mean-square-velocity/
Last updated: 2026-10-30

> The root mean square velocity calculator finds the rms speed of molecules of a gas at a given temperature from its molar mass, with values for common gases.

## Inputs

- Gas
- Molar mass M (g/mol)
- Temperature T (K, °C, °F)

## Results

- Molar mass
- RMS velocity
- Mean speed

## Formula

```
v_rms = √(3RT/M)
```

## Explanation

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

FieldWhat to enterGasChoose one: Air, Nitrogen N₂, Oxygen O₂, Hydrogen H₂ …Molar mass M (g/mol)A numberTemperature TUnits: 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)14.48506.708721.72506.708728.97506.708736.21506.708743.45506.708757.93506.7087

## 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.

## FAQ

**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).


## Sources

- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)