# 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 ${\displaystyle t}$ (in hours) required for sedimentation of a fraction with a known sedimentation coefficient ${\displaystyle s}$ (in svedbergs):

${\displaystyle t={\frac {k}{s}}}$

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

${\displaystyle k={\frac {\ln(r_{\rm {max}}/r_{\rm {min}})}{\omega ^{2}}}\times {\frac {10^{13}}{3600}}}$

As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:[1]

${\displaystyle k={\frac {2.53\cdot 10^{5}\times \ln(r_{\rm {max}}/r_{\rm {min}})}{({\rm {{RPM}/1000)^{2}}}}}}$

Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the ${\displaystyle k}$ factor of a centrifuge-rotor combination.

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

${\displaystyle 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 ${\displaystyle S}$ by the formula:

${\displaystyle T={\frac {K}{S}}}$

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

${\displaystyle {\frac {T_{1}}{K_{1}}}={\frac {T_{2}}{K_{2}}}}$

Where ${\displaystyle T_{1}}$ is the time to pellet in one rotor, and ${\displaystyle K_{1}}$ is the K-factor of that rotor. ${\displaystyle K_{2}}$ is the K-factor of the other rotor, and ${\displaystyle T_{2}}$, 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.