How this calculator works
The three-dimensional Maxwell speed distribution has different RMS, mean, median and peak speeds. The median divides the population into equal halves; it is not the most probable speed at the distribution peak. All four scale with sqrt(RT/M). Molecular-weight presets use NIST WebBook data, with CIPM reference dry air. The model describes dilute classical gas in equilibrium, without bulk flow.
Formula
vrms = sqrt(3RT/M); vmean = sqrt(8RT/(pi M)); vpeak = sqrt(2RT/M); vmedian = 1.5381722544550522 sqrt(RT/M).
Worked example
For a custom M = 0.02494338785445972 kg/mol at 300 K, sqrt(RT/M) is sqrt(100000) m/s: RMS speed is 547.7225575 m/s and mean speed is 504.6265044 m/s. Raising temperature to 1200 K doubles every speed.
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Frequently asked questions
Why are mean and RMS speeds different?
Squaring gives faster particles more weight, so RMS speed is larger than mean speed.
Is median the distribution peak?
No. Median splits the probability in half; the peak is the most probable speed.
Why is average velocity not reported?
In the rest frame of an equilibrium gas, the vector average velocity is zero even though mean speed is positive.