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.