Centrifuge Sedimentation Time Calculator
Enter particle, liquid, and rotor geometry values to estimate whether the selected speed can pellet the target particles. The calculator also reverses the equation for required RPM and particle-size cutoff.
Estimated sedimentation time1.16
- Required RPM for target time
- 1,021
- Particle-size cutoff
- 0.34
- RCF at starting radius
- 804.96
- RCF at pellet radius
- 1,509.3
- Maximum radial velocity
- 1.36
- Outer-radius Reynolds number
- 0
- Model validity
- Strong Stokes-regime match
Assumes dilute, rigid, spherical particles in a Newtonian liquid with terminal Stokes motion.
Use radii measured from the rotation axis to the starting liquid position and the intended pellet position.
How to use this calculator
- Enter the particle diameter and the effective particle density.
- Enter the liquid density and dynamic viscosity at the centrifugation temperature.
- Measure the starting and pellet radii from the rotation axis, not from the tube wall.
- Enter the planned RPM and target time, then compare the predicted time, cutoff, RCF range, and validity notes.
How the sedimentation time is calculated
This calculator applies the integrated Stokes-law expression for a spherical particle moving through a centrifugal field. Because centrifugal acceleration increases with radius, the calculation uses both the starting radius and the pellet radius instead of a single average radius.
The inputs are first converted to SI units: particle diameter from micrometers to meters, densities from g/mL to kg/m³, viscosity from mPa·s to Pa·s, and radii from centimeters to meters. With particle density ρp, liquid density ρm, viscosity η, particle diameter d, inner radius ri, outer radius ro, and rotor speed N in RPM, the angular speed is:
ω = 2πN / 60
The ideal sedimentation coefficient for a rigid sphere is:
s = d²(ρp − ρm) / (18η)
Stokes motion in the rotor is dr/dt = sω²r. Integrating from ri to ro gives:
t = ln(ro / ri) / (sω²)
The required RPM for a target time T is found by rearranging the same expression:
Nrequired = (60 / 2π) × sqrt(18η ln(ro / ri) / (d²(ρp − ρm)T))
The particle-size cutoff solves for d at the entered speed and target time. Particles larger than the cutoff are predicted to traverse the entered radial interval; smaller ideal spheres are predicted to remain short of the pellet position.
What moves the result most
Diameter and RPM have the largest leverage because both enter as squared terms. Doubling particle diameter or rotor speed cuts the ideal sedimentation time by about a factor of four. Viscosity slows settling directly, while the particle-liquid density difference speeds it directly. The radius term is logarithmic, but it still matters when a sample starts near the rotor axis or must travel to a much larger pellet radius.
RCF and model checks
Relative centrifugal force is shown at both radii using RCF = 1.118 × 10^-5 × r × N², where r is in centimeters. The outer-radius value is higher because centrifugal acceleration grows with radius. The maximum radial velocity is evaluated at the outer radius, and the outer-radius Reynolds number is reported to check the creeping-flow assumption. Reynolds numbers below 0.1 are a strong match for Stokes flow, values from 0.1 through 1 deserve caution, and values above 1 are likely outside the model's valid range.
What this calculator leaves out
The calculation assumes dilute, noninteracting, rigid spherical particles in a Newtonian liquid. It does not include hindered settling, aggregation, flocculation, Brownian diffusion, wall effects, concentration gradients, tube angle interception, or non-Newtonian sample behavior. Real particles such as cells, rods, plates, soft aggregates, and irregular minerals can pellet more slowly than the ideal result.
Worked example
For 1 µm particles with density 2.65 g/mL in water-like liquid at 0.998 g/mL and 1.002 mPa·s, starting at 8 cm and pelleting at 15 cm, a speed of 3000 RPM gives an estimated travel time of 1.16 minutes. The RCF rises from about 805 ×g at the starting radius to about 1509 ×g at the pellet radius.
For a 10 minute target time with the same inputs, the required speed is about 1021 RPM. At 3000 RPM for 10 minutes, the ideal spherical cutoff is about 0.34 µm, so larger ideal particles are predicted to complete the entered radial travel.
Common questions
How do I calculate centrifugation time from particle size and RPM?
Use the particle diameter, particle density, liquid density, liquid viscosity, starting radius, pellet radius, and RPM in the integrated Stokes equation. The result is proportional to viscosity and the logarithm of the radius ratio, and inversely proportional to particle diameter squared, density difference, and RPM squared.
What RPM will pellet particles of a given diameter?
The required RPM comes from rearranging the same sedimentation equation for speed at the target time. Treat it as a process estimate only, and never exceed the rated limits for the centrifuge, rotor, bucket, adapter, or tube.
How do fixed-angle and swinging-bucket rotors affect the radius measurements?
The equation needs the radial distance from the rotation axis to the starting position and to the intended pellet position. In a fixed-angle rotor, particles may hit the tube wall before reaching the nominal tube bottom, so the entered pellet radius should represent the actual radial travel path you mean to model.
What particle sizes remain in the supernatant after centrifugation?
The cutoff diameter is the ideal spherical diameter predicted to traverse the entered radial interval during the target time. Smaller particles may remain in the supernatant under the model assumptions, while larger particles are predicted to pellet.
When is Stokes law valid for centrifugal sedimentation?
Stokes law is most appropriate for dilute suspensions of small rigid spheres at low Reynolds number. This calculator reports the outer-radius Reynolds number because that is where velocity is highest; values below 0.1 are the strongest match, while values above 1 are likely outside creeping-flow behavior.