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Centrifuge k-Factor and Pelleting Time Calculator

Calculate a rotor's k-factor (clearing factor) from its radii and speed, estimate the time to pellet a particle of known S value, and convert a run time to another rotor.

Formula

ω=2π rpm60\omega = \dfrac{2\pi\,\mathrm{rpm}}{60}
k=ln⁡(rmax⁡/rmin⁡)ω2×10133600k = \dfrac{\ln(r_{\max}/r_{\min})}{\omega^{2}}\times\dfrac{10^{13}}{3600}
t (h)=ks,s in Svedberg unitst\,(\mathrm{h}) = \dfrac{k}{s},\qquad s\ \text{in Svedberg units}
t2=t1 k2k1t_2 = t_1\,\dfrac{k_2}{k_1}
kk
clearing factor: the time in hours for a particle of 1 S to pellet
rmax⁡, rmin⁡r_{\max},\ r_{\min}
radii from the axis to the bottom of the tube and to the liquid surface, in cm
ω\omega
angular velocity, in rad/s
ss
sedimentation coefficient, in Svedberg units (1 S = 10⁻¹³ s)

How it works

The k-factor summarises how efficiently a rotor pellets particles at a given speed: it is the time, in hours, needed to sediment a particle with a sedimentation coefficient of 1 S from the liquid surface to the bottom of the tube. A rotor with a short path length and a high speed has a low k-factor and pellets quickly.

Dividing k by a particle's S value gives the time it needs. Because k is the same for any particle in a given rotor, the time for a protocol written for one rotor is scaled to another by the ratio of their k-factors. The k-factor is specified by the manufacturer at maximum speed, and scales as 1/rpm² below that.

Worked example

A rotor has rmax = 8.4 cm and rmin = 3.4 cm and runs at 12,000 rpm. A particle sediments at 100 S.

  1. ω = 2π × 12,000 / 60 = 1,256.6 rad/s.
  2. k = ln(8.4 / 3.4) / 1,256.6² × 10¹³ / 3600 = 1,591.
  3. t = 1,591 / 100 = 15.91 h.

The k-factor is 1,591 and the particle would take about 15.9 hours to pellet, so this speed is not practical for a 100 S particle.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The particle sediments freely in a dilute suspension, at the sedimentation coefficient measured in the medium used.
  • The tube is filled to the level the radii describe. A fuller or emptier tube changes rmin and so the k-factor.
  • Acceleration and deceleration times are not included.

Common mistakes

  • Using the k-factor from the data sheet at a lower speed without scaling it by 1/rpm².
  • Converting a run time between rotors with different fill levels or tube types.
  • Treating the pelleting time as exact. Viscosity, density, concentration and tube shape all change it.

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Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.