# Clearing factor

In centrifugation the clearing factor or k factor represents the relative pelleting efficiency of a given centrifuge rotor at maximum rotation speed. It can be used to estimate the time $t$ (in hours) required for sedimentation of a fraction with a known sedimentation coefficient $s$ (in svedbergs):

$t={\frac {k}{s}}$ The value of the clearing factor depends on the maximum angular velocity $\omega$ of a centrifuge (in rad/s) and the minimum and maximum radius $r$ of the rotor:

$k={\frac {\ln(r_{\rm {max}}/r_{\rm {min}})}{\omega ^{2}}}\times {\frac {10^{13}}{3600}}$ As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:

$k={\frac {2.53\cdot 10^{5}\times \ln(r_{\rm {max}}/r_{\rm {min}})}{({\rm {{RPM}/1000)^{2}}}}}$ Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the $k$ factor of a centrifuge-rotor combination.

For runs with a rotational speed lower than the maximum rotor-speed, the $k$ factor has to be adjusted:

$k_{\rm {adj}}=k\left({\frac {\mbox{maximum rotor-speed}}{\mbox{actual rotor-speed}}}\right)$ 2

The K-factor is related to the sedimentation coefficient $S$ by the formula:

$T={\frac {K}{S}}$ Where $T$ is the time to pellet a certain particle in hours. Since $S$ is a constant for a certain particle, this relationship can be used to interconvert between different rotors.

${\frac {T_{1}}{K_{1}}}={\frac {T_{2}}{K_{2}}}$ Where $T_{1}$ is the time to pellet in one rotor, and $K_{1}$ is the K-factor of that rotor. $K_{2}$ is the K-factor of the other rotor, and $T_{2}$ , the time to pellet in the other rotor, can be calculated. In this manner, one does not need access to the exact rotor cited in a protocol, as long as the K-factor can be calculated. Many online calculators are available to perform the calculations for common rotors.