Calculator Inputs
Overall page flow stays single column. The input area uses a responsive three, two, and one column grid.
Example Data Table
These reference values use 300 K and the molar-mass form of the ideal-gas equation.
| Gas | Temperature (K) | Molar Mass (g/mol) | RMS Speed (m/s) |
|---|---|---|---|
| Helium (He) | 300 | 4.0026 | 1,367.3108 |
| Dry Air | 300 | 28.97 | 508.2344 |
| Oxygen (O₂) | 300 | 31.998 | 483.5896 |
| Carbon Dioxide (CO₂) | 300 | 44.01 | 412.3468 |
Formula Used
Molar-mass form: vrms = √(3RT / M)
Particle-mass form: vrms = √(3kBT / m)
Average speed: vavg = √(8RT / πM)
Most probable speed: vmp = √(2RT / M)
Here, T is absolute temperature in Kelvin, R is the universal gas constant, kB is the Boltzmann constant, M is molar mass in kg/mol, and m is particle mass in kg. The calculator also derives energy values from kinetic theory.
How to Use This Calculator
- Select a gas preset or keep the gas custom.
- Choose whether you want the molar-mass or particle-mass formula.
- Enter temperature and pick the matching unit.
- Provide molar mass or particle mass, depending on the chosen basis.
- Adjust precision and chart settings if needed.
- Press Calculate RMS Speed to place the result above the form.
- Review the speed metrics, energy values, consistency check, and Plotly chart.
- Use CSV or PDF buttons to export your session history.
Frequently Asked Questions
1) What does rms speed mean?
RMS speed is the square root of the mean of squared molecular speeds. It weights faster molecules more strongly than a simple arithmetic average, so it is always higher than the most probable speed.
2) Does pressure affect rms speed?
For an ideal gas, pressure does not directly change rms speed when temperature stays fixed. Speed depends on temperature and molecular mass. Pressure mainly changes number density unless temperature also changes.
3) Why convert temperature to Kelvin?
Temperature in Kelvin works directly in the equations. Celsius and Fahrenheit are converted to Kelvin first because absolute temperature is required for kinetic theory formulas.
4) How is rms speed different from average speed?
RMS speed uses the square-root mean of squared speeds. Average speed is the mean of all speeds. Most probable speed is the peak of the Maxwell-Boltzmann distribution.
5) Why do lighter gases move faster?
Lighter gases move faster at the same temperature. Because molar mass appears in the denominator, decreasing mass raises the calculated rms speed.
6) Can I use this for real gases?
No. These formulas assume ideal-gas behavior. At very high pressures or very low temperatures, real-gas effects can make the result less accurate.
7) What does the chart represent?
The chart shows the Maxwell-Boltzmann speed distribution. It helps you see how speed values spread around the most probable, average, and rms speeds for the selected state.
8) Why export CSV or PDF?
CSV is useful for spreadsheets and batch review. PDF is better for sharing, printing, or attaching a formatted calculation snapshot to reports.