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Root Mean Square Speed Calculator

Work out root mean square speed instantly with clear inputs, formula shown and shareable results.

About Root Mean Square Speed Calculator

Kinetic theory gives the root mean square speed as sqrt(3RT/M). Nitrogen at 300 K averages 517 m/s - faster than a rifle bullet. The Maxwell-Boltzmann distribution also defines a mean speed of sqrt(8RT/piM) and a most probable speed of sqrt(2RT/M), which sit in the ratio 1.225 : 1.128 : 1.

Formulas

RMS speed

v(rms) = sqrt(3 R T / M)

Distribution speeds

v(mean) = sqrt(8RT/piM); v(mp) = sqrt(2RT/M)

Worked example

With the default values below, Root Mean Square Speed Calculator returns Root Mean Square Speed of 516.83. Change any input above and every figure here is recalculated in your browser.

Inputs used

Temperatureminimum 0 K
300 K
Molar mass of the gasminimum 0 g/mol
28.014 g/mol

Results

Root Mean Square Speed
516.83 m/s
Mean Speed
476.17 m/s
Most Probable Speed
421.99 m/s
RMS Speed In km/h
1,860.6

Step by step

  1. 1Values used
  2. 2RMS speed
  3. 3Distribution speeds
  4. 4Root Mean Square Speed= 516.83 m/s
  5. 5Mean Speed= 476.17 m/s
  6. 6Most Probable Speed= 421.99 m/s
  7. 7RMS Speed In km/h= 1,860.6

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why are there three different speeds?

The Maxwell-Boltzmann distribution is skewed, so its peak, mean and root-mean-square all differ. RMS is the one tied to kinetic energy.

If molecules move that fast, why does a smell take time to cross a room?

Because they collide constantly - billions of times a second - so the net progress is a slow random walk rather than a straight dash.

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