Sedimentation Coefficient (Svedberg) Calculator
Find the sedimentation coefficient in svedberg units from boundary movement in an analytical ultracentrifuge, plus RCF and molar mass.
🌀 What is a Sedimentation Coefficient?
The sedimentation coefficient is the ratio of a particle's terminal sedimentation velocity to the centrifugal acceleration driving it, s = u ÷ (ω²r). Because the numerator is a speed and the denominator is an acceleration, the coefficient has units of time. For macromolecules those times are extraordinarily short, so the field adopted the svedberg unit, defined as exactly 10⁻¹³ seconds and named after Theodor Svedberg, who built the first analytical ultracentrifuge in the 1920s and received the 1926 Nobel Prize in Chemistry for it.
Sedimentation coefficients are how molecular biologists name a great deal of cellular machinery. The bacterial ribosome is the 70S ribosome, assembled from 50S and 30S subunits. The eukaryotic counterpart is 80S, from 60S and 40S. Spliceosomal snRNPs, virus particles, lipoprotein classes and immunoglobulin oligomers all carry S-value labels. In the laboratory the coefficient is measured by watching a sharp concentration boundary migrate outward in a spinning cell, either by absorbance or by interference optics, and fitting its radial position over time.
The most common misconception is that S values add. They do not, which is why a 50S and a 30S subunit produce a 70S ribosome rather than an 80S one. The coefficient is proportional to the buoyant mass divided by the frictional coefficient, and combining two particles increases the mass while also increasing the drag, so the assembled complex always sediments more slowly than the naive sum suggests. A second frequent error is comparing raw s values measured in different buffers or at different temperatures. Published values should be corrected to standard conditions, water at 20 degrees C, and written s20,w.
This calculator handles the full chain of arithmetic. From rotor speed and the two boundary radii it computes the angular velocity, the sedimentation coefficient in both seconds and svedbergs, and the relative centrifugal field at the mean boundary position. Given a diffusion coefficient, a partial specific volume and a solvent density it then applies the Svedberg equation to return an absolute molar mass, and plots how the boundary migrates outward through the run.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A 105 kDa Protein Complex at 50,000 RPM
50,000 RPM, r₁ = 6.0 cm, r₂ = 6.5 cm, t = 60 min, D = 6.9 × 10⁻⁷ cm²/s, v̄ = 0.73, ρ = 0.998, 20°C
Example 2 — Lysozyme, a Small Globular Protein
60,000 RPM, r₁ = 5.9 cm, r₂ = 6.0 cm, t = 39 min, D = 1.04 × 10⁻⁶ cm²/s, v̄ = 0.703, ρ = 0.998, 20°C
Example 3 — The 70S Bacterial Ribosome
20,000 RPM, r₁ = 5.5 cm, r₂ = 6.4 cm, t = 82 min, D = 1.9 × 10⁻⁷ cm²/s, v̄ = 0.66, ρ = 1.05, 4°C
❓ Frequently Asked Questions
🔗 Related Calculators
What is a sedimentation coefficient?
The sedimentation coefficient s is the terminal sedimentation velocity of a particle divided by the applied centrifugal acceleration, s = u / (omega^2 r). It has units of seconds and is almost always quoted in svedberg units where 1 S = 1e-13 s. It captures how quickly a particle settles under a given centrifugal field.
How do I calculate the sedimentation coefficient from boundary movement?
Use s = ln(r2/r1) / (omega^2 t), where r1 and r2 are the boundary radii at the start and end of the run, omega is the angular velocity in rad/s, and t is the elapsed time in seconds. The logarithm appears because the boundary accelerates as it moves outward into a stronger field.
What is a svedberg unit?
A svedberg (symbol S) is 1e-13 seconds, named after Theodor Svedberg who built the first analytical ultracentrifuge and won the 1926 Nobel Prize in Chemistry for the work. Ribosomes, ribosomal subunits and many viruses are routinely named by their S values, such as the 70S bacterial ribosome.
Why do 50S and 30S subunits combine into a 70S ribosome, not an 80S one?
Because sedimentation coefficients are not additive. s is proportional to buoyant mass divided by the frictional coefficient, and joining two particles increases the mass but also increases the drag. The assembled ribosome is more compact than the two subunits considered separately, so its s value falls short of the arithmetic sum.
How do I convert RPM to angular velocity?
omega = 2 x pi x RPM / 60 radians per second. A rotor at 50,000 RPM turns at about 5,236 rad/s. Centrifugal acceleration goes as omega squared, so doubling the rotor speed quadruples the field and cuts the run time for a given boundary movement by a factor of four.
What is RCF and how is it different from RPM?
RCF, the relative centrifugal field, is the acceleration expressed in multiples of Earth's gravity: RCF = omega^2 r / g. RPM alone is meaningless for comparing protocols because the field also depends on rotor radius. Two rotors at the same RPM deliver very different RCF if their radii differ.
What is the Svedberg equation for molar mass?
M = sRT / [D(1 - v-bar rho)], where s is the sedimentation coefficient, R the gas constant, T absolute temperature, D the diffusion coefficient, v-bar the partial specific volume of the particle, and rho the solvent density. It links a hydrodynamic measurement to an absolute molar mass without needing standards.
What is the partial specific volume v-bar?
It is the volume increase per gram of solute added to the solution, in cm3/g. For most globular proteins it is close to 0.73 cm3/g, for nucleic acids about 0.55 cm3/g, and for lipoproteins it can exceed 1 cm3/g, which is why lipoproteins float rather than sediment.
Why does the buoyancy term matter so much?
The buoyancy factor (1 - v-bar rho) sets the effective driving mass. With v-bar = 0.73 cm3/g in water it is only about 0.27, so a protein experiences barely a quarter of the force its dry mass would suggest. When v-bar rho reaches 1 the particle is neutrally buoyant and never sediments at all.
What temperature should I enter?
Enter the actual temperature of the run, usually 20 degrees C for a standard analytical ultracentrifugation experiment or 4 degrees C for a cold run. Temperature enters both the RT term of the Svedberg equation and the frictional coefficient, and it also changes solvent viscosity and density.