Buoyancy Calculator - Will It Float, and How Deep?

Problem: will it float, and how much can it carry?

You have an object, a rough idea of its size and weight, and a question the formula does not answer on its face. Will this block ride high or low? How much can a float take before it goes under? How heavy will that stone be once it is below the surface and you are the one pulling the rope? Archimedes' principle answers all three, but only once the volume, the mass and the fluid are in the same units, and that is where most hand calculations go wrong.

The buoyant force on anything under the surface equals the weight of the fluid it pushes aside. One liter of fresh water weighs 9.807 N, so a sealed one-liter object is pushed up with 9.807 N in fresh water and 10.05 N in seawater, whatever it is made of. A 1 ft³ box pushes aside 62.43 lb of fresh water. The calculator takes the whole volume of your object, the fluid, and optionally its mass, and returns the force, the verdict and the depth it settles at.

Solution: compare two densities, not two weights

Weight alone says nothing about floating. A 10 kg block of pine floats and a 1 kg steel bar sinks, because what decides it is the object's average density, its mass divided by its whole volume, set against the density of the fluid. Enter both and the calculator does the comparison for you.

One verdict, three states. Floats, sinks, or neutral when the two densities are within a thousandth of each other, which is the state a submarine or a diver's weight belt is tuned for.

The number that follows the verdict. For a floater, how much of it sits under the surface and how much more it can carry. For a sinker, how much it weighs in the water, which is the load on a rope, a winch or a lifting bag.

Nine fluids at once. The same object is run through air, gasoline, oil, fresh water, seawater, milk, Dead Sea water, glycerin and mercury, so you can see where it changes its mind.

Getting the volume and the density of an awkward object

The calculator needs the volume of the whole object, and for a box that is simple: a cooler measuring 30 × 20 × 15 cm on the outside encloses 9 L. For a stone, a casting or a piece of driftwood there are two ways that work at home, and the second one also hands you the density directly.

Displacement. Fill a container to the brim, stand it in a tray, push the object fully under and measure the water that spills over. The spilled volume is the object's volume. It is the method from the Archimedes story, and it works for anything that does not soak up water.

Weighing in water. Hang the object from a luggage scale or a spring scale, note the reading, then lower it until it is fully under water without touching the bottom and note the reading again. The drop is the mass of water pushed aside, so in fresh water every gram of drop is a milliliter of volume. A kitchen scale works the other way round: set a bowl of water on it, zero it, and lower the object on a string until it is fully under without touching the bowl; the reading that appears is the mass of water pushed aside. An object that reads 500 g in air and 300 g in water has a volume of 200 mL and a density of 2,500 kg/m³, two and a half times that of water. In pounds the arithmetic is the same: 1.2 lb in air and 0.8 lb in water is 181.4 mL, or 11.07 in³, and a density three times that of water.

Reading in air	Reading in water	Volume	Density relative to water
500 g	300 g	200 mL	2.5
1.2 lb	0.8 lb	181.4 mL	3
20 kg	12.6 kg	7.4 L	2.703

The rule behind the table: density relative to water equals the reading in air divided by the drop. Two things spoil the measurement. Air bubbles clinging to the surface add volume that is not the object's, so tap it or wet it first. And anything porous, from pumice to unsealed wood, takes in water during the weighing and reads heavier than it is; weigh it quickly, or seal it, and repeat.

This is also the check behind the old story of the king's crown: pure gold is about 19.3 times as dense as water, so a crown of it loses about one nineteenth of its weight when weighed under water. A crown that loses noticeably more has something lighter mixed in, whatever it looks like on the outside.

From the object in your hand to the verdict

Fluid - pick one of the nine, or choose the last entry and type a density from a datasheet in kg/m³, g/cm³ or lb/ft³.
Volume of the whole object - in liters, milliliters, cubic meters, US gallons, cubic feet or cubic inches. Not the part under water: the calculator works that out. For a box, multiply the three outside dimensions; for an odd shape, measure the water it displaces when pushed fully under.
Mass - optional, in kilograms, grams or pounds. Without it you get the buoyant force and the fluid displaced; with it, the verdict.
Read the result - the force when fully submerged, the mass of fluid pushed aside, the verdict with its follow-up number, and the nine-fluid table.

Decision table: what your density ratio means

Divide the object's average density by the fluid's. That one ratio decides everything, and the table below shows what each band looks like in practice. The highlighted row is the band most floating objects people ask about fall into.

Density ratio	What happens	Under the surface	Case from this page
up to 0.5	floats high	half or less	pine-like block, 50.0 %
0.5 to 0.9	floats, mostly under	50 to 90 %	loaded cooler in seawater, 78.1 %
0.9 to 0.999	floats low, little spare lift	90 to 99.9 %	ice, 91.7 %; a water-density body in the sea, 97.6 %
within 0.1 % of 1	neutral, hovers	all of it, at any depth	a water-density body in fresh water
above 1.001	sinks	all of it	stone, fluid carries 37.9 %; steel, 12.7 %

For a floater the ratio IS the fraction under the surface. For a sinker its inverse is the share of the weight the fluid carries, which is why a steel part feels only slightly lighter in water while a stone feels noticeably lighter.

Examples from real situations

A 20-liter block that weighs 10 kg, in a lake. Its density is 500 kg/m³, in the range of many softwoods. It floats exactly 50.0 % under, and it can carry another 10 kg (22.05 lb) before its top reaches the water. Fully pushed under, the lake pushes back with 196.1 N.

A cooler of 1 ft³ loaded to 50 lb, dropped in the ocean. It floats 78.1 % under, with 21.9 % showing. Seawater would carry another 13.99 lb (6.345 kg) before it disappears, so a few more cans is the whole margin.

A liter of ice. At 917 kg/m³ it floats 91.7 % under in fresh water and 89.5 % in seawater, which leaves 8.3 % and 10.5 % showing. That is where "only the tip of the iceberg" comes from.

70 kg in 70 liters, close to the average density of a human body with air in the lungs. In fresh water that is neutral. Real bodies sit close to this line, which is why most people float low with full lungs and slowly sink after breathing out. In seawater it floats 97.6 % under with 1.75 kg of spare lift. In the Dead Sea it floats 80.6 % under, 19.4 % above, and could hold another 16.8 kg.

A 20 kg stone of 7.4 liters, lifted from the seabed. Its density works out to 2,703 kg/m³, about that of granite. On deck it weighs 196.1 N; under water it weighs 121.7 N (27.37 lbf), because the sea carries 37.9 % of it. The moment it breaks the surface, the rope takes the full weight.

A liter of steel. 7.85 kg in a liter is 7,850 kg/m³. It sinks in everything on the list except mercury, and under fresh water it still weighs 67.18 N (15.1 lbf): the water carries only 12.7 %.

Two cubic meters of anything, in air. Air pushes up with 24.03 N, the weight of 2.45 kg. That is the whole budget a balloon of that size has for its envelope, its gas and whatever it carries.

Cheat sheet: lift per liter and per gallon

The lift one unit of volume gets in each fluid, fully submerged. Multiply by your object's volume and compare with its weight; the calculator does exactly this, but the table is quicker for a rough check on the spot.

Fluid	kg/m³	lb/ft³	N per liter	lbf per gallon
Air at sea level	1.225	0.07647	0.01201	0.01022
Gasoline	750	46.82	7.355	6.259
Vegetable oil	920	57.43	9.022	7.678
Fresh water	1,000	62.43	9.807	8.345
Seawater	1,025	63.99	10.05	8.554
Milk	1,030	64.3	10.1	8.596
Dead Sea water	1,240	77.41	12.16	10.35
Glycerin	1,261	78.72	12.37	10.52
Mercury	13,546	845.6	132.8	113

Densities are typical values near room temperature. Fresh water is taken at 1,000 kg/m³, its value when cold; at 68°F it is 998.2, a difference of under two tenths of a percent. Gasoline, oil and milk vary by a few percent between products, and seawater by region.

What readers ask about floating

Why does the calculator want the whole volume, not the part under water?

Because the part under water is the answer, not the input. A floater sinks until it has pushed aside its own mass of fluid; the 10 kg block settles into exactly 10 L of lake. Entering the submerged part as if it were the whole would describe an object that cannot exist.

Does a heavy object always sink?

No. A ship of many thousands of tons floats because its hull encloses a huge volume of air, so its average density is below that of seawater. A 1 kg steel bar sinks because 1 kg of steel fits into about 0.13 L. Mass per volume decides, not mass.

Is it easier to float in the sea than in a lake?

Yes, by the ratio of the densities. Seawater at 1,025 kg/m³ gives 2.5 % more lift than fresh water. For a body that is just neutral in a lake, that is 1.75 kg of spare lift in the sea; in the Dead Sea it is 16.8 kg.

Would something float differently on another planet?

The verdict and the depth would not change, because gravity multiplies the weight and the buoyant force by the same factor. Only the forces in newtons would. This calculator uses standard Earth gravity, 9.80665 m/s².

How heavy is a sunken object when I pull it up?

While it is fully under, its weight minus the buoyant force: the 20 kg stone pulls with 121.7 N in seawater. As it breaks the surface the fluid lets go, and the load rises to the full 196.1 N. Plan the rope for the dry weight.

What about a boat that takes on water, or a sponge?

Those change their own average density as they fill: the water inside adds mass without adding volume. The calculator assumes a rigid, sealed object. For a leaking hull, add the mass of the water it has taken on and run it again.

Does air really push things up?

It does, just weakly: 0.01201 N per liter, or 24.03 N on two cubic meters. That is enough to lift a helium balloon and small enough that it is ignored for everyday weighing, though precision scales correct for it.

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