How can you determine whether an object will float?

You compare not weight but average density. You divide the total mass of an object by its total volume, including any air volume inside, and compare that result to the density of a liquid. If the density is less it floats; if more it sinks; if equal it stays at whatever depth you put it in. The density of fresh water is about 1000 kg per cubic meter while that of sea water is about 1025 kg. So a ship will tend to float higher in the ocean than in a river.

What is buoyancy? Why am I negative net buoyant?

The net buoyancy is the difference between the mass of fluid displaced by an object and the mass of the object itself. A positive value represents a force pushing the object upwards, and can be expressed as weight that could be supported by one hand. A negative value means the object will sink because it weighs more than the fluid it displaces. The absolute value of this quantity directly indicates how much buoyancy is required to raise or how much weight needs to be reduced in order for objects to have neutral buoyancy.

How much helium is needed to lift a kilo?

At sea level you need about .95 cubic meters or 950 liters. Helium displaces 1.225 kg of air per cubic meter and weighs about .169 kg so it can lift about 1.056 kg. This does not take into account the weight of balloons, string, and attachments for payload. All this uses up the same budget for payload. Hydrogen's lifting power is only about 8% more but not twice as much. What actually matters is not the ratio of densities but the difference in density from air.

What is a ship's displacement and how is it calculated?

Displacement is the weight of water displaced by a ship and for a floating ship it equals its own weight. To estimate underwater volume, multiply the length at the waterline times the width of the ship at the waterline, then times draft and shape factor, then times density of water. Use draft of hull itself. For sail ships this is to bottom of keel not to bottom of skeg. As a skeg increases depth without significantly changing volume results would be greatly exaggerated.

Why is 90% of an iceberg below water?

The proportion of a floating object below the surface is equal to its density divided by that of the fluid. Sea ice has a density of about 917 kilograms per cubic meter, and seawater has a density of 1025. If you divide 917 by 1025, you get 0.895. So about 89% or 90% of the volume is below the surface, with only one-tenth above it. The same calculation shows that 73% of an oak log and 23% of cork are under water.

Buoyancy Calculator

Choose the situation

What are you working out

An object in a liquid

A balloon or airship in air

A boat hull from its dimensions

The object and its fluid

Fluid

Density is what decides everything here, and it moves with temperature and salinity. Sea water runs from about 1020 in the Baltic to 1029 in the Red Sea, so use a measured figure when the margin is tight.

Volume of the object

What you know about it

Its mass or weight

Its average density

Mass of the object

Gravity

Your answer

Net buoyancy (positive floats up)

Buoyant force when fully submerged

Net buoyancy

Please input values into the fields

Buoyant force, fully submerged: N
Weight of the object: N
Net force, up is positive: N

Mass of fluid displaced: kg
Average density of the object: kg/m³
Density relative to the fluid

Share of it under the surface: %
Volume under the surface: m³
Volume above the surface: m³

Extra load before it goes under: kg

It floats. At 750 against the fluid's 1000 kg per cubic metre, 75 percent of its volume sits below the surface and the rest stands proud.

Add 5 kg and it goes under.

You are in fresh water, the least forgiving case. Sea water at 1025 kg per cubic metre would give this object 2.5 percent more buoyancy, which is why a boat rides higher once she leaves the river.

What the numbers look like

Buoyancy is the upward force experienced by an object in a fluid. Its magnitude exactly equals the weight of the displaced fluid. This statement is Archimedes' principle and solves all problems on this page.

The difference in applications is which values are already known, either on the income or expenditure side. A diver adjusting the ballast of a ROV (Remotely Operated Vehicle) knows the volume and weight and wants to find the difference. An airship pilot knows the conditions of the gas balloon and wants to calculate the payload. A ship owner knows the conditions of the hull and wants to determine the displacement.

This calculator has three modes because the underlying physics is the same but the way it's calculated is different.

All basic formulas:

The buoyancy acting on an object immersed in a liquid is the product of the density of the liquid, the volume of displaced liquid and the acceleration due to gravity.

F_B = \rho_{\text{fluid}} \times V_{\text{displaced}} \times g

The unit for density is kilograms per cubic meter, the unit for volume is cubic meters, the unit for acceleration due to gravity is m/s2, and the unit for the result is newtons.

A sealed box with a volume of 0.02 cubic meters is fully submerged in fresh water. The displaced water weighs 20 kilograms, calculated as the product of 0.02 and 1000, while the buoyancy force corresponds to 196.2 Newtons, calculated as the product of 20 and 9.81.

Also pay attention to information that is not included in the formula. The type of material an object is made from, how deep it is submerged or its shape are all ignored by the formula. A cubic meter of lead and a cubic meter of polystyrene completely submerged in the same water will experience the exact same buoyancy; their only difference is weight.

Compare densities instead of weights to determine if something floats.

If the average density of an object is less than that of the liquid it will float. The average density is calculated by dividing the total mass by the total volume and includes any airspace. This explains why a ship made from iron can float while an iron nail cannot.

\rho_{\text{object}} = \frac{m}{V} \qquad \text{floats when } \rho_{\text{object}} < \rho_{\text{fluid}}

We still have the same box with a volume of 0.02 cubic meters but this time it weighs 15 kilograms. The average density is 750 kilograms per cubic meter which is the result of dividing 15 by 0.02. Compared to fresh water's density of 1000, the ratio of densities is 0.75 so it floats.

You can't tell anything by weight alone. An aircraft carrier may weigh a hundred thousand tons and still float while a wedding ring weighing only five grams will not float.

Buoyancy and why this value is important.

Once both values are known, one is subtracted from the other. The resulting value is net buoyancy and indicates which direction an object will move.

\text{net buoyancy} = \rho_{\text{fluid}} V - m \qquad [\text{kg}]

F_{\text{net}} = (\rho_{\text{fluid}} V - m)\, g \qquad [\text{N}]

Manufacturers of submersibles often quote the net buoyancy in kilograms rather than newtons because this is the unit used when weighing ballast on a scale. For example, if a box displaces 20 kg of water and weighs 15 kg itself, it has a net buoyancy of 5 kg. When submerged, it will exert an upward force of 5 kg.

A positive value means buoyancy. A negative value means sinking and the absolute value of a negative number indicates how much more buoyancy is required or weight reduction is needed to float again.

Zero means neutral buoyancy. This is a state that divers and ROV operators strive for. In reality this is often an unstable condition as objects which are neutrally buoyant at the surface tend to become heavier with depth, as pressure further compresses air volume.

How much of a floating object is under water?

Floating objects sink until the weight of water displaced is equal to their own weight. The proportion submerged therefore corresponds to the difference in density.

\frac{V_{\text{submerged}}}{V_{\text{total}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}}

The numbers for icebergs can be derived from this. Sea ice has a density of about 917 kilograms per cubic meter, while seawater weighs about 1025 kg. If you divide 917 by 1025, you get 0.895. Therefore, approximately 90% of an iceberg is below the surface of the water.

Floating in sea water	Density (kg/m3)	Fraction submerged
Balsa wood	160	16 percent
Cork	240	23 percent
Pine	500	49 percent
Oak	750	73 percent
Ice	917	89 percent
Human body, lungs full	960	94 percent

The last line explains why a person floating has only their face above water and why they sink when they exhale. This is because the volume decreases by several liters when they exhale, which makes the average density just slightly more than that of water.

The buoyancy of balloons and airships is a difference, not a relation.

A balloon works in a similar way to a ship but uses air instead of water. The buoyancy is the product of volume and the difference between the density of outside air and the gas inside.

\text{gross lift} = (\rho_{\text{air}} - \rho_{\text{gas}}) \times V \qquad [\text{kg}]

The density of air at sea level is about 1.225 kg per cubic meter at a temperature of 15 degrees Celsius. As the density of helium under the same conditions is about 0.169, one cubic meter of helium can carry about 1.056 kg.

These numbers explain a common surprising fact: although hydrogen is half as dense as helium, this does not mean that the buoyancy doubles. What matters is the difference from air. While going from 0.169 to 0.085 halves the difference, going from 1.056 to 1.140 only increases it by about 8%.

Gas	Molar mass (g/mol)	Density at 15 C (kg/m3)	Lift per cubic metre (kg)
Hydrogen	2.02	0.085	1.140
Helium	4.00	0.169	1.056
Hot air at 100 C	28.96	0.946	0.279
Methane	16.04	0.678	0.547
Ammonia	17.03	0.720	0.505

A party balloon with a diameter of 28 centimeters contains approximately 0.0115 cubic meters of gas, giving helium a lift capacity of about 12 grams before subtracting the mass of the latex and ribbons. To keep an average adult off the ground would require thousands of such balloons.

Hot air balloons

Hot air balloons do not require any special gas at all. By heating the air inside, it expands and some escapes through vents, leaving the remaining air less dense than the outside air. At constant pressure, density is inversely proportional to absolute temperature.

\rho_{\text{inside}} = \rho_{\text{outside}} \times \frac{T_{\text{outside}}}{T_{\text{inside}}} \qquad (T \text{ in kelvin})

The temperature inside a typical hot air balloon is about 100 degrees Celsius, while the outside temperature is 15 degrees Celsius. Converted to Kelvin this is 373 and 288 respectively, which gives a ratio of 0.772. So the density of the air inside is 0.946 kilograms per cubic meter, giving an upthrust of 0.279 kilograms per cubic meter.

To carry objects in this way requires a large volume. A gas tank with a volume of 2800 cubic meters, about the size of a typical four-person balloon, will generate an overall lift of approximately 780 kilograms. This explains why balloons are so huge and airships not much smaller.

It also explains why it is important to pick the right day for flying. Hot air balloonists launch at sunrise because the outside air is cooler and denser, which creates a greater density difference and thus lift without added weight.

Displacement volume, form factor and cargo weight

A floating hull displaces a volume of water equal to its own weight. The displacement volume is not a replacement for the ship's weight but another way of measuring the same thing, and it was also the traditional method of determining a ship's weight.

To determine the actual underwater volume of a hull drawings are required. However to get a quick answer the industry uses a shape factor. This is how much of the box around the hull in water that is actually taken up by the hull.

C_B = \frac{\nabla}{L \times B \times T} \qquad\Longrightarrow\qquad \nabla = L \times B \times T \times C_B

\Delta = \rho \times \nabla

L is the length of the waterline, B the width of the ship at the waterline and T the draft of the hull. The calculated volume figure is given in cubic metres. The first formula is correct by definition. The value used for the shape factor is an estimate.

Hull	Typical block coefficient
Barge, pontoon or box hull	0.85 to 0.95
Tanker or bulk carrier	0.78 to 0.85
General cargo ship	0.65 to 0.75
Trawler, tug or workboat	0.55 to 0.65
Displacement motor cruiser	0.45 to 0.55
Planing powerboat at rest	0.40 to 0.50
Cruising sailboat, canoe body	0.35 to 0.45
Fine racing or catamaran hull	0.30 to 0.40

With a waterline length of 6 meters, a width of 2.4 meters and a draft of 0.5 meters, with the shape factor being 0.4, the volume is 2.88 cubic meters. In freshwater it's 2880 kilograms, in saltwater 2952 kilograms. This difference of 72 kilograms occurs with the same hull and waterline, where only the salt content differs.

The amount of water extracted corresponds to the weight.

A ship that displays a displacement of 10 tons has a weight of 10 tons. The buoyancy force that makes it float is therefore 98,065 newtons, which is the product of 10,000 and 9.81. This completes the calculation.

This is important to note because it's easy to accidentally double count a calculation. Do not multiply the volume of water by the density of water again. The density of water was already used to convert the underwater volume into tons, and using it again will increase your answer by a factor of about one thousand.

A mistake that invalidates this calculation.

For sailboats draft refers to the keel tip. In this formula it however refers to the hull itself and only measures down to the bottom of a canoe-like hull. A fin keel adds more than a meter to the draft but hardly increases volume. If you were to use the depth of the keel here, that would lead to an overestimation of the displacement volume by a factor of two or more.

Payload weight.

The remaining value, after subtracting the displacement at a given waterline and taking into account mass already on board, is how much weight can be added; this includes crew, fuel, water, supplies, and equipment. Shipbuilding engineers call this the deadweight tonnage.

This calculator also gives the amount of cargo weight required to raise draft by another inch. This value is obtained from a rectangular model with constant coefficient but since actual hull becomes slimmer as it goes deeper into water you should consider this an optimistic estimate.

Commonly used densities of liquids:

All the answers on this page are directly dependent on the density of the liquid, so it is worth finding out exactly what that value is. The values below are representative for conditions close to room temperature and standard atmospheric pressure.

Fluid	Density (kg/m3)	Note
Air at 15 C	1.225	Standard sea level atmosphere
Petrol or gasoline	750	Varies with blend and temperature
Ethanol	789
Vegetable or cooking oil	918	Floats on water
Fresh water at 4 C	1000	The densest fresh water gets
Fresh water at 25 C	997
Brackish or estuary water	1005 to 1020	Mixes by the tide
Sea water	1020 to 1029	Baltic at the low end, Red Sea high
Milk, whole	1030
Glycerine	1260
Mercury	13534	Iron floats on it

Water reaches its maximum density not at the freezing point but at 4 degrees Celsius. This is a special property that explains why the surface of water freezes while the bottom of lakes does not and why fish can survive in winter.

Lift outside of Earth

Buoyancy varies with gravity so it is less on the moon and more on Jupiter. However whether an object floats or sinks does not change because the weight of the object also changes in proportion so the two effects cancel each other out.

Place	Gravity (m/s2)
Earth, standard	9.80665
Moon	1.62
Mars	3.72
Jupiter, cloud tops	24.79
Sun, surface	274

The waterline of an object floating on a lake on Mars is exactly the same as it would be on Earth. However, lifting an object out of the water surface is easier.

Here's how to use this calculator.

First select the appropriate situation. For Object in Fluid enter volume and either mass or average density. For Air Balloon or Zeppelin enter volume of gas container, gas, and structural weight. For Ship Hull enter three dimensions and shape of ship hull.

Each field has a special function to switch the units so you can use liters and kilograms or cubic feet and pounds without having to manually convert.

The result fields fill out gradually according to your inputs; non-relevant fields are not shown with zero values but simply remain blank. The chart area below shows the same results over a range of values. If you submerge an object into six different liquids, the charts show buoyancy before sinking, lift from various common gases and displacement volume as a function of draft.

The scope of this model is:

The calculations assume that the liquid is at rest and has a uniform density, and that the volume of the object does not change. In reality there are three factors which can invalidate these assumptions.

Compressible objects: Wetsuits, buoyancy compensators or tanks with air bubbles will compress under increasing pressure and thus reduce the volume of water displaced by the object, making it heavier and sinking deeper.
Surface tension: Very small or light objects can float on the surface of water even though they should sink. This is why a needle floats and a water strider can run across the surface of water.
Air bubbles and wetting: Objects with trapped air bubbles displace more water than their own volume until the air bubbles escape. This explains why a small capsized boat will first float up before sinking to an upright position.

These factors do not change the principle itself but only the volume used when applying the principle.

The values given here are for planning and learning purposes. The density of water, air, and commercial materials varies with temperature, pressure, salinity, and quality. The square coefficient is a representative value for certain hull shapes and does not correspond to the values you measured for your own boat. Information on buoyancy, diving behavior, and permissible capacity of ships should be checked based on actual measurement data and relevant standards.

Frequently asked questions

How can you determine whether an object will float?: You compare not weight but average density. You divide the total mass of an object by its total volume, including any air volume inside, and compare that result to the density of a liquid. If the density is less it floats; if more it sinks; if equal it stays at whatever depth you put it in. The density of fresh water is about 1000 kg per cubic meter while that of sea water is about 1025 kg. So a ship will tend to float higher in the ocean than in a river.
What is buoyancy? Why am I negative net buoyant?: The net buoyancy is the difference between the mass of fluid displaced by an object and the mass of the object itself. A positive value represents a force pushing the object upwards, and can be expressed as weight that could be supported by one hand. A negative value means the object will sink because it weighs more than the fluid it displaces. The absolute value of this quantity directly indicates how much buoyancy is required to raise or how much weight needs to be reduced in order for objects to have neutral buoyancy.
How much helium is needed to lift a kilo?: At sea level you need about .95 cubic meters or 950 liters. Helium displaces 1.225 kg of air per cubic meter and weighs about .169 kg so it can lift about 1.056 kg. This does not take into account the weight of balloons, string, and attachments for payload. All this uses up the same budget for payload. Hydrogen's lifting power is only about 8% more but not twice as much. What actually matters is not the ratio of densities but the difference in density from air.
What is a ship's displacement and how is it calculated?: Displacement is the weight of water displaced by a ship and for a floating ship it equals its own weight. To estimate underwater volume, multiply the length at the waterline times the width of the ship at the waterline, then times draft and shape factor, then times density of water. Use draft of hull itself. For sail ships this is to bottom of keel not to bottom of skeg. As a skeg increases depth without significantly changing volume results would be greatly exaggerated.
Why is 90% of an iceberg below water?: The proportion of a floating object below the surface is equal to its density divided by that of the fluid. Sea ice has a density of about 917 kilograms per cubic meter, and seawater has a density of 1025. If you divide 917 by 1025, you get 0.895. So about 89% or 90% of the volume is below the surface, with only one-tenth above it. The same calculation shows that 73% of an oak log and 23% of cork are under water.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Archimedes' principle
The statement of the principle and its derivation from the pressure difference across a submerged body.
Wikipedia: Buoyancy
Buoyant force, apparent weight, stability of floating bodies and the density conditions for floating, sinking and neutral buoyancy.
Wikipedia: Lifting gas
Lift per unit volume for hydrogen, helium, methane, ammonia and heated air, and the molar mass basis for comparing them.
Wikipedia: Block coefficient
Definition of the hull coefficients used in naval architecture, including the block coefficient this calculator applies.
NOAA: Why is the ocean salty?
Salinity of sea water and how it varies between ocean basins, which sets the density used in the marine cases.
NIST: SI base units and standard gravity
Standard acceleration of gravity and the SI definitions behind the newton, the kilogram and the cubic metre.