Gas molecules zip around at hundreds of metres per second, with a spread of speeds described by the Maxwell–Boltzmann distribution. Lighter particles move faster at the same temperature – why hydrogen escapes from Earth’s atmosphere.
How to use the Particle Velocity Calculator
- Particle mass
- Temperature
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the particle mass (in atomic mass units, molar mass or kg) 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 |
|---|---|
| Particle mass | Units: u (g/mol), kg, mₑ |
| Temperature | Units: K, °C, °F |
What each result means
- Most probable speed = sqrt(2×1.380649e-23×[Temperature]÷[Particle mass])
- Mean speed = sqrt(8×1.380649e-23×[Temperature]÷(pi×[Particle mass]))
- Root-mean-square speed = sqrt(3×1.380649e-23×[Temperature]÷[Particle mass])
- Mean kinetic energy = 1.5×1.380649e-23×[Temperature]÷1.602176634e-19×1000
Example values
How the main result changes when Particle mass changes and everything else stays at the example values above:
| Particle mass (u (g/mol)) | Root-mean-square speed (m/s) |
|---|---|
| 14.01 | 722.5204 |
| 21.01 | 589.9354 |
| 28.01 | 510.8991 |
| 35.02 | 456.962 |
| 42.02 | 417.1473 |
| 56.03 | 361.2602 |
Formula
v_p = √(2k_BT/m), v̄ = √(8k_BT/(πm)), v_rms = √(3k_BT/m)Worked example
Inputs — Particle mass: 28.014 u (g/mol); Temperature: 293.15 K.
Results — Most probable speed = 417.14734 m/s; Mean speed = 470.70037 m/s; Root-mean-square speed = 510.89906 m/s; Mean kinetic energy = 37.89257 meV.
Key terms
- Maxwell–Boltzmann distribution
- Speed distribution of particles in a gas.
Frequently asked questions
Why are there three different speeds?
The distribution is skewed: v_p < v̄ < v_rms.
How fast are nitrogen molecules at room temperature?
About 510 m/s (rms).
Does mass affect average kinetic energy?
No – it depends only on temperature.
Why do light gases escape planets?
Their speeds can exceed the escape velocity.
What formula does the Particle Velocity Calculator use?
v_p = √(2k_BT/m), v̄ = √(8k_BT/(πm)), v_rms = √(3k_BT/m).