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Root Mean Square Speed Calculator.

Calculate ideal-gas molecular RMS speed from absolute temperature and molar mass.

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RMS speed: 516.962846 m/s

RMS speed

0.000000m/s

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Use Cases

Physics homework and exam prep

Quickly compute RMS speed for ideal gas problems in kinetic theory, helping verify manual calculations and understand temperature/mass effects.

Example: Find RMS speed of helium (4 g/mol) at 300 K.

Engineering gas behavior analysis

Estimate molecular speeds in gas systems for design or safety considerations, such as in vacuum technology or gas flow calculations.

Example: Estimate RMS speed of nitrogen at 500 K for a high-temperature process.

Frequently Asked Questions

What is root mean square speed?
Root mean square (RMS) speed is a measure of the average speed of particles in an ideal gas. It is calculated as the square root of the average of the squares of the speeds of all molecules. It gives a representative speed that relates to the gas's temperature and molar mass.
How is RMS speed calculated?
The RMS speed is calculated using the formula: v_rms = sqrt(3RT/M), where R is the ideal gas constant (8.314 J/(mol·K)), T is the absolute temperature in kelvin, and M is the molar mass in kilograms per mole. This calculator uses that formula directly.
Why is molar mass in kg/mol?
The formula for RMS speed requires molar mass in kilograms per mole to be consistent with the SI units of the gas constant (J/(mol·K)). Using grams per mole would give incorrect results. This calculator expects kg/mol for accurate output.

Tips & Common Mistakes

Tips

  • Ensure temperature is in kelvin (K). If you have Celsius, add 273.15 to convert.
  • Convert molar mass to kg/mol. For example, if you have g/mol, divide by 1000.
  • Use the ideal gas constant R = 8.314 J/(mol·K) for consistent units.
  • Remember that RMS speed is an average; individual molecules move at various speeds.

Common Mistakes to Avoid

  • Using molar mass in g/mol instead of kg/mol, leading to results off by a factor of sqrt(1000).
  • Forgetting to convert temperature to kelvin, using Celsius directly.
  • Confusing RMS speed with average speed or most probable speed; they are different statistical measures.

Last updated: August 13, 2026