Centrifuge k-Factor Calculator: Convert Run Time When Switching Rotors
“20,000 × g for 30 minutes” — that specification breaks down the moment you change rotors.
RCF only tells you how much force is applied, not how far the particles have to travel. The same centrifugal force will pellet particles in a few millimetres inside a short-path angle rotor, yet require particles to traverse more than ten centimetres in a long-path swinging-bucket rotor. How long sedimentation takes depends on the combination of force and path length — that combination is the k-factor (clearing factor).
Formula
k = 2.53 × 10¹¹ × ln(r_max / r_min) ÷ rpm²
r_max and r_min are the outermost and innermost radii of the sample in the rotor (cm); rpm is the rated maximum speed.
The ln(r_max/r_min) term captures path length — the logarithm arises because particles speed up as they move outward (centrifugal force increases with radius), so the outer portion of the journey takes less time than the inner portion.
A smaller k means faster sedimentation.
This formula is verifiable: for the Beckman SW 41 Ti, r_min = 6.71 cm, r_max = 15.30 cm, rated speed 41,000 rpm — substituting gives 124.1, and the manufacturer’s published k is 124. This tool uses exactly that equation; you can verify it against your own rotor’s datasheet.
Converting Run Time When Switching Rotors
New run time = Original time × (k_new ÷ k_original)
Run time scales linearly with k — it is that straightforward. The harder part is remembering that the conversion is necessary — matching RCF while ignoring k is the most common way centrifugation protocols break down when transferred between labs.
To give a sense of scale: an angle rotor with k = 40 and a swinging-bucket rotor with k = 130, run at the same RCF, require 3.25× more time in the swinging-bucket rotor for equivalent sedimentation. A 30-minute protocol copied without conversion is less than one-third complete.
The Speed Penalty Is Squared
k is defined at the rated maximum speed. When running at a lower speed:
k_actual = k_rated × (rated speed ÷ actual speed)²
The squared term is easy to underestimate. Halving the speed multiplies k by 4, and the required run time by 4 as well — “a bit slower, a bit longer” usually means far more than most people expect. This tool calculates the multiplier directly.
Estimating Time Directly from Sedimentation Coefficient
If the sedimentation coefficient s of your target particle is known (in Svedberg units; 1 S = 10⁻¹³ s):
Sedimentation time (hours) = k ÷ s
Svedberg values for ribosomal subunits, viral particles, and macromolecular complexes are available in the literature. Note that this estimates the time to pellet completely; practical protocols typically include a safety margin.
When k Is Not Sufficient
- k assumes sedimentation in a homogeneous medium. In density-gradient or rate-zonal centrifugation, where medium density varies with radius, k provides only an order-of-magnitude estimate.
- Different manufacturers may define r_min differently (tube mouth vs. actual meniscus); take care when comparing k values across manufacturers.
- A particle’s sedimentation coefficient depends on the density and viscosity of the medium; it shifts when you change the buffer.
Related Tools
For converting between rotor speed and relative centrifugal force, see RCF / RPM Calculator. For estimating cell concentration after pelleting, see OD₆₀₀ Cell Density Converter. For supernatant and pellet volume calculations, see Dilution Calculator.
FAQ
Why does run time need to be recalculated when I switch rotors if the RCF is the same?
Because RCF only tells you how hard the particles are being pushed, not how far they have to travel. The same centrifugal force will pellet particles in a few millimetres in a short-path angle rotor, yet the sample must travel more than ten centimetres in a long-path swinging-bucket rotor. Sedimentation time depends on the combination of force and path length — that combination is the k-factor. Two rotors can deliver the same RCF while differing in k by more than threefold — copying the run time without adjusting means less than one-third of the sedimentation is actually complete.
What is the k-factor formula and how do I verify the result?
k = 2.53 × 10¹¹ × ln(r_max / r_min) ÷ rpm², where rpm is the **rated maximum speed**. To verify, use a rotor whose k has been published: for the Beckman SW 41 Ti, r_min = 6.71 cm, r_max = 15.30 cm, rated speed 41,000 rpm — the formula gives 124.1, and the published value is 124. This tool uses exactly that equation; you can check it against your own rotor's datasheet.
Why does the path-length term use a logarithm?
Because centrifugal force increases linearly with radius — as particles move outward, the driving force grows and they accelerate. The outer portion of the path therefore takes less time than the inner portion, and the cumulative relationship is logarithmic rather than a simple difference in radii. This also explains why r_min matters so much: the further the starting point is from the axis, the longer the slowest segment of the journey.
If I halve the rotor speed, is doubling the run time enough?
Far from it — you need four times as long. k is inversely proportional to the square of rotor speed: k_actual = k_rated × (rated speed ÷ actual speed)². Halving the speed multiplies k by 4, so the required run time also increases fourfold. This squared penalty is easy to underestimate — "a bit slower, a bit longer" usually means much more than most people expect.
Can I estimate run time directly from the sedimentation coefficient?
Yes, as an estimate: sedimentation time (hours) = k ÷ s, where s is the sedimentation coefficient in Svedberg units (1 S = 10⁻¹³ s). Svedberg values for ribosomal subunits, viral particles, and macromolecular complexes are available in the literature. Keep in mind this estimates the time to pellet completely; practical protocols typically add a safety margin. Also note that s depends on medium density and viscosity, so it shifts when you change the buffer.
Does the k-factor work for density-gradient centrifugation?
Only as an order-of-magnitude guide. The k-factor derivation assumes a homogeneous medium, whereas in density-gradient and rate-zonal centrifugation the medium density varies with radius, changing the local sedimentation velocity throughout the run. For these applications, follow equivalent conditions from the literature or the manufacturer, and confirm with a pilot run if precision matters.
Can k values from different manufacturers be compared directly?
With caution: r_min definitions vary. Some manufacturers measure from the tube mouth, others from the actual meniscus — the same rotor yields a different k depending on which convention is used. When comparing across manufacturers, it is safest to recalculate using a consistent definition rather than dividing two published values directly.
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