Buoyant Force on Macromolecule Calculator
Find the buoyant force, weight and net sedimenting force acting on one macromolecule in solution, at gravity or in a centrifuge.
⚖️ What is the Buoyant Force on a Macromolecule?
The buoyant force on a macromolecule is the upward push that a protein, nucleic acid or virus particle experiences from the solvent it displaces, exactly as Archimedes described for a ship or a stone. The magnitude is Fb = ρVa, the mass of displaced solvent times the acceleration acting on it. Subtracting it from the molecule's own weight gives the net force that actually drives sedimentation: Fnet = (M ÷ NA) × a × (1 − v̄ρ), where the bracketed term is called the buoyancy factor.
This single factor explains a surprising amount of laboratory biochemistry. It is why analytical ultracentrifugation needs fields of hundreds of thousands of g rather than ordinary gravity, why sedimentation coefficients change when you swap H₂O for D₂O, and why caesium chloride density gradients separate DNA from RNA from protein so cleanly. It is also why plasma lipoproteins are isolated by flotation rather than sedimentation, and why the Svedberg equation carries a (1 − v̄ρ) term rather than the bare molar mass.
The common misconception is that buoyancy is negligible for something as small as a single molecule. In fact it is enormous in relative terms. A globular protein has a partial specific volume near 0.73 cm³/g, so in water the product v̄ρ is about 0.73 and the buoyancy factor is only about 0.27. Roughly three quarters of the molecule's weight is cancelled before any net motion begins. A second misconception is that a stronger centrifuge somehow overcomes buoyancy. It does not, because both weight and buoyancy scale with the same acceleration, so the ratio between them never changes.
This calculator converts molar mass in kilodaltons to the mass and volume of one molecule, then reports the weight, the buoyant force, the net sedimenting force, the buoyancy factor and the neutral buoyancy density where the molecule would stop moving altogether. It plots the net force as the solvent density is swept through the neutral point, and tabulates how all three forces scale across centrifugal fields from 1 g to 500,000 g.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Serum Albumin Under Ordinary Gravity
M = 66.5 kDa, v̄ = 0.734 cm³/g, ρ = 0.998 g/cm³, field = 1 × g
Example 2 — Lysozyme at 200,000 × g in an Ultracentrifuge
M = 14.3 kDa, v̄ = 0.703 cm³/g, ρ = 0.998 g/cm³, field = 200,000 × g
Example 3 — DNA Near Its Banding Density in Caesium Chloride
M = 1,000 kDa, v̄ = 0.55 cm³/g, ρ = 1.7 g/cm³, field = 1 × g
❓ Frequently Asked Questions
🔗 Related Calculators
What is the buoyant force on a macromolecule?
It is the upward force a molecule feels from the solvent it displaces, F = rho x V x a, where rho is the solvent density, V the molecular volume and a the acceleration. For a 66.5 kDa protein in water at 1 g the buoyant force is about 7.9e-22 N, roughly three quarters of the molecule's own weight.
How do I calculate the net force on a molecule in solution?
Subtract buoyancy from weight: F_net = m x a - rho x V x a, which simplifies to F_net = (M / N_A) x a x (1 - v-bar rho). The bracket is the buoyancy factor. Enter molar mass in kilodaltons, partial specific volume in cm3/g and solvent density in g/cm3.
What is the buoyancy factor (1 - v-bar rho)?
It is the fraction of a molecule's weight that survives buoyancy. With v-bar = 0.73 cm3/g in water at 0.998 g/cm3 the factor is 0.272, so a protein sediments as if it had only 27 percent of its actual mass. The same term appears in the Svedberg equation for sedimentation.
What is the partial specific volume v-bar?
The partial specific volume is the volume a solution gains per gram of solute added, expressed in cm3/g. It is the reciprocal of the effective density of the solute inside the solution. Globular proteins average about 0.73 cm3/g, nucleic acids about 0.55 cm3/g, and lipids and lipoproteins exceed 1 cm3/g.
At what solvent density is a macromolecule neutrally buoyant?
At rho = 1 / v-bar. A protein with v-bar = 0.73 cm3/g is neutrally buoyant at 1.37 g/cm3, and DNA with v-bar = 0.55 cm3/g bands near 1.82 g/cm3. In an equilibrium density gradient every species migrates to the layer whose density matches its own buoyant density and stops there.
How big is the buoyant force compared with molecular thermal motion?
At 1 g it is tiny. The net force on a 66.5 kDa protein is roughly 2.9e-22 N, so over a nanometre it does about 3e-31 J of work, which is a hundred million times smaller than kT at room temperature. This is why proteins do not settle out of solution on their own and need an ultracentrifuge.
Does the buoyant force change in a centrifuge?
Yes, in magnitude. Both weight and buoyancy scale directly with the applied acceleration, so a 200,000 g field multiplies each by 200,000. The ratio between them, and therefore the buoyancy factor and the direction of net motion, is completely unchanged.
Why do lipoproteins float instead of sinking?
Because their partial specific volume exceeds 1 cm3/g, the product v-bar rho is greater than 1 in an ordinary aqueous buffer, so the buoyancy factor is negative and the net force points toward the rotor axis. Clinical flotation ultracentrifugation exploits exactly this to separate HDL, LDL and VLDL.
How do I convert kilodaltons to the mass of a single molecule?
Divide by Avogadro's number after converting to grams per mole. A 66.5 kDa protein is 66,500 g/mol, so one molecule weighs 66,500 / 6.022e23 = 1.104e-19 g, which is 1.104e-22 kg. The calculator handles this conversion for you.
What is the molecular volume used in this calculation?
V = M x v-bar / N_A, the anhydrous volume the molecule occupies in solution. For a 66.5 kDa protein with v-bar = 0.734 cm3/g that is about 81 nm3, equivalent to a sphere of radius 2.68 nm. Real proteins are not spheres, so treat the radius as an order-of-magnitude guide.