Root mean square speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula v_\mathrm{rms} = \sqrt {{3RT}\over{M_m}} where vrms is the root mean square speed, Mm is the molar mass of the gas, R is the molar gas constant, and T is the temperature in kelvins. source: http://en.wikipedia.org/wiki/Root_mean_square_speed

RMS velocity equation

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <msub> <mi>v</mi> <mstyle mathvariant="normal"> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mstyle> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <mn>3</mn> <mo>&InvisibleTimes;</mo> <mi>R</mi> <mo>&InvisibleTimes;</mo> <mi>T</mi> </mrow> <msub> <mi>M</mi> <mi>m</mi> </msub> </mfrac> </msqrt> </mrow> </math>

v_\mathrm{rms} = \sqrt {{3RT}\over{M_m}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <msub> <mi>v</mi> <mstyle mathvariant="normal"> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mstyle> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <mn>3</mn> <mi>R</mi> <mi>T</mi> </mrow> <msub> <mi>M</mi> <mi>m</mi> </msub> </mfrac> </msqrt> </mrow> <annotation encoding="SnuggleTeX">\[ v_\mathrm{rms} = \sqrt {{3RT}\over{M_m}} \]</annotation> </semantics> </math>

RMS error

root mean squared error