Buoyancy Calculator

buoyant force = fluid density × displaced volume × g object weight = mass × g submerged fraction = mass ÷ ( fluid density × object volume )

ρ

Density of the fluid, in kg/m³ — 1,000 for fresh water, 1,025 for sea water, 13,546 for mercury. The field also takes g/cm³ and lb/ft³

V

Volume of the object in litres — the field also takes millilitres, cubic metres, cubic feet, cubic inches and gallons. This is the object's total volume, not the part that ends up underwater

m

Mass of the object in kilograms — the field also takes pounds, tonnes and grams. Nothing here is weight: the weight is computed from it as mg and printed separately

g

Standard gravity, 9.80665 m/s² — the same value throughout, so the page describes a body in Earth's gravity and not on the Moon or in orbit

Vd

Displaced volume — the part of the object below the surface. It is the only volume that produces buoyancy, and it is capped at the object's own volume, which is exactly why dense things sink

Use this page when you need to know whether something floats, how much of it will be underwater, or how much lift a fluid can provide — a boat's displacement, a life jacket, a float, a buoy, a diver's weighting, ice on water, or a tank of something denser than water. It is also the page for the counter-intuitive cases: a steel ship floats while a steel bolt does not, and it is the same formula both times, with the difference entirely in the volume. Two habits make the answers more useful. First, read the submerged fraction rather than the verdict badge, because it is the number that carries the design: 60 percent submerged is a boat with freeboard, 99 percent is a boat that is about to stop being one, and the badge calls both of them floating. Second, remember that only the submerged volume displaces anything. A floating object's buoyancy always equals its weight exactly — that is not a coincidence, it is what makes it float — so the interesting question is never whether they balance but how much of the object has to go under for them to.

1. A block of wood, 3 litres and 1.8 kg, in fresh water

   1. Weight: 1.8 × 9.80665 = 17.652 N
   2. Submerged fraction: 1.8 ÷ (1,000 × 0.003) = 0.60, so 60 percent of the block goes under
   3. Displaced volume: 0.60 × 3 = 1.8 L
   4. Buoyant force: 1,000 × 0.0018 × 9.80665 = 17.652 N
   5. Net force: 17.652 − 17.652 = 0 — it floats
   6. The remaining 1.2 L, 40 percent of the block, stays above the surface

   The buoyant force and the weight come out identical, and that is not a coincidence to be checked — it is what floating means. Only the submerged 1.8 litres displace anything, so the displaced volume is whatever it takes to balance the weight, and the page solves for it rather than assuming it. Note also that the 3 litre figure never appears in the buoyancy calculation. It only sets the ceiling: if the block needed more than 3 litres of displacement it would sink, and 60 percent says this one is nowhere near that.

2. An aluminium block, 2 litres and 5.4 kg

   1. Weight: 5.4 × 9.80665 = 52.956 N
   2. Submerged fraction: 5.4 ÷ (1,000 × 0.002) = 2.70 — more than 1, so the block cannot float and the page caps it at 100 percent
   3. Displaced volume: 2 L, the whole block
   4. Buoyant force: 1,000 × 0.002 × 9.80665 = 19.613 N — the maximum this block can ever get from water
   5. Net force: 19.613 − 52.956 = −33.343 N, acting downwards
   6. The 33.3 N shortfall is what the seabed has to make up once it lands

   The interesting number here is the fraction the page refuses to print: 2.70, or 270 percent submerged. That is the honest answer to 'how much would have to go under', and it is impossible, which is exactly why aluminium sinks. The −33.343 N is the force the object feels while fully submerged and unsupported; once it settles on the bottom the seabed supplies it and the object is in equilibrium again, just not a floating one. Compare this with the 3 litre wood block above: raising the volume to 12 litres would make the same 5.4 kg float, and that is the whole trick behind a steel hull.

3. A litre of ice in sea water

   1. Weight: 0.917 × 9.80665 = 8.993 N
   2. Submerged fraction: 0.917 ÷ (1,025 × 0.001) = 0.895, so 89.5 percent is underwater
   3. Displaced volume: 0.895 L
   4. Buoyant force: 1,025 × 0.000895 × 9.80665 = 8.993 N
   5. Net force: 0 — it floats
   6. Above the surface: 10.5 percent of the block, and of an iceberg

   Ice is 917 kg/m³ and sea water is 1,025, and that ratio is the famous 'nine tenths below the waterline' — here it comes out at 89.5 percent, which is the same statement with the rounding done. The page also shows why the figure is not a constant: the same litre of ice in fresh water sits at 91.7 percent submerged, because fresh water is less dense and has to be pushed aside in a larger quantity to carry the same weight. That difference between 89.5 and 91.7 percent is a real effect in polar waters, and it is the kind of thing the reference table's two water rows exist to make visible.

The page gives the static answer — whether the object floats, and how far it settles — and says nothing about stability. A floating body can be in balance and still capsize, because that depends on where its centre of gravity is relative to the centre of the displaced volume, and none of that is in this calculation; a log and a canoe can show the same 60 percent submerged with completely different behaviour in a wave. It assumes the fluid is uniform and that the object is rigid: a stratified fluid, a partly filled tank, or a flexible hull that changes shape as it settles is not described. It takes no account of anything attached to the object — a mooring line in tension, a swimmer holding on, a load on the deck — all of which change the balance without changing the buoyancy. Surface tension is ignored, which matters for anything small enough to be held up by it: an insect, a needle, a grain of sand, where the real behaviour has nothing to do with Archimedes. The page is also entirely static in the other sense: it assumes the object has come to rest, and a body moving through a fluid, accelerating upwards, or being dropped into it passes through states this calculation does not describe. It uses a single value of g, so it is a calculation for the Earth's surface and not for a body in orbit, where everything is effectively buoyant and nothing sinks. Finally, density here is a single number per fluid, so temperature and salinity are folded into whatever value you type rather than being tracked — sea water at 4 °C is denser than the 1,025 used in the table, and that difference is measurable.

What is the buoyancy formula?

The buoyant force equals the weight of the fluid displaced: F = ρ × Vd × g, where ρ is the fluid density, Vd is the submerged volume and g is 9.80665 m/s². A 3 litre block of wood weighing 1.8 kg pushes aside 1.8 litres of fresh water, which weighs 17.652 N, so that is the upward force and it exactly balances the block's own 17.652 N of weight.

Will it float or sink?

Compare the object's density with the fluid's. Below the fluid's density it floats, with the submerged fraction equal to the ratio of the two — 0.5 kg per litre in water floats at 50 percent submerged; equal to it, the object hovers fully submerged; above it, the object sinks and no amount of orientation helps. A 2 litre aluminium block weighing 5.4 kg has a density of 2,700 kg/m³ against water's 1,000, so it sinks with 33.3 N of its weight unaccounted for.

Why does a steel ship float when a steel bolt does not?

Because the ship is mostly air. Flotation depends on the object's average density, not on what it is made of: a hull enclosing a large volume of air has an average density well below water's, so it floats, while a solid bolt has steel's 7,850 kg/m³ and cannot. The same arithmetic applies to both — a 1 litre steel block needs 7.85 litres of displacement to float and only has 1, so it sinks with 67.2 N to spare.

What does the submerged fraction tell me?

It is the proportion of the object below the surface, and it equals the object's density divided by the fluid's. A floating object's buoyancy always equals its weight, so this fraction is simply whatever it takes to get there — nothing about the object's size enters it. Read it as the margin: 60 percent means 40 percent of the object is still above water and there is room to load it further; 95 percent means the next wave or the next kilogram puts it under.

What is neutral buoyancy?

It is the case where the object's density equals the fluid's, so it is fully submerged and the net force is exactly zero — it neither rises nor sinks, and stays where you put it. The page badges it separately from floating, and the distinction matters: a fully submerged body in balance is a submarine or a diver at trim, not a boat. Anything with the same density as water qualifies, which is why a diver adjusts buoyancy with air in a jacket rather than by carrying weights alone.

Does the buoyant force depend on how deep the object is?

No, not for an incompressible fluid. The pressure on the bottom of a submerged object is greater than on the top, and the difference — which is what buoyancy is — depends only on the object's height, not on its depth. A block at one metre and the same block at a hundred metres feel the same upward force; what changes with depth is the absolute pressure on every face, which crushes things rather than lifting them. The page is therefore depth-independent by construction, and it has no field for depth because none is needed.

• Archimedes' Principle (College Physics 2e, §11.7) — the buoyant force as the weight of the displaced fluid, and floating as the case where it equals the object's weight — OpenStax
• Buoyancy — the relation between submerged fraction and the ratio of densities, and the distinction between neutral buoyancy and a body resting on the bottom — Wikipedia
• NIST Guide to the SI — the densities of water and mercury in kg/m³, standard gravity as 9.80665 m/s², and the exact factors behind the litre, the cubic foot and the pound used above — National Institute of Standards and Technology