Buoyant Force Calculator

Ships can float and you feel lighter in a swimming pool for the same reason. This is buoyancy, or the upward force exerted by a fluid on any object immersed in it. This calculator computes this force based on the density of the liquid, the volume displaced by the object, and the gravity at that location.

If you enter three of the four fields, the tool will calculate the fourth. This allows you to work backwards from known forces to find out the density of an unknown liquid, for example. If you enable the "Check buoyancy" function, you'll also get information on whether a particular object floats or sinks.

What is buoyancy?

When an object is immersed in a liquid it displaces some of the liquid. According to Archimedes' principle, the upward force acting on the object will be equal to the weight of the liquid displaced by the object.

This force is created by the pressure. Since the pressure in a liquid increases with depth, the bottom of an immersed object experiences more pressure than its top. This difference creates a resultant upward force whose magnitude is equal to the weight of the displaced fluid.

If the buoyancy exceeds the weight of the object it floats. If the weight is greater, the object sinks. When they are equal, the object remains stationary. This is the state of neutral buoyancy that submarines and divers strive to achieve.

This is how this calculation tool works:

By default the tool calculates buoyancy. Enter the density of the fluid, displaced volume and acceleration due to gravity to get key results in newtons. The mass of the displaced fluid is also shown.

To calculate the density just leave the field for Density blank and enter Force, Volume and Gravity. The same goes for other parameters.

This conversion tool is good to identify an unknown liquid based on a measured force. Each field accepts metric or imperial units which are converted before calculation. Gravity can be entered in meters per second squared (m/s²) or g.

Understanding the formula:

The buoyancy is equal to the product of the density of the fluid, displaced volume and gravitational acceleration.

where F_b is the buoyancy force in Newtons, ρ is the density of the fluid in kilograms per cubic meter, V is the displaced volume in cubic meters and g is the acceleration due to gravity in meters per second squared. Since ρ multiplied by V gives the mass of the displaced fluid, this formula essentially represents the weight of that displaced fluid.

Let's consider a cubic meter of fresh water with a density of 1,000 kilograms per cubic meter and an acceleration due to gravity of 9.81 meters per second squared.

This is equivalent to about 9.81 kilonewtons which is the weight of one tonne of mass. This makes sense as a cubic metre of water has a mass of approximately one tonne. The buoyancy experienced by a diver who displaces 0.07 cubic metres of seawater will be less.

As this is approximately equivalent to a person's weight of 72 kilograms, divers with a body weight close to this value can almost float peacefully in the water.

Does it float, does it sink or stay?

Whether an object floats depends on the interplay of two forces: buoyancy, which acts upwards, and the weight of the object itself, which pulls downwards. When you activate the "Check Buoyancy" function and enter the mass of an object, the calculation tool compares these two forces.

For a quick estimate, you can check the average density. If the value calculated by dividing the mass of the object by its volume is less than that of the liquid, it will float; if it's more, it will sink; and if it's equal, it'll remain at any depth. A lump filled with iron will sink because the density of iron is much higher than water. Conversely, an iron ship floats because the hollow hull displaces a large volume of water, lowering its average density below that of water.

The mass of displaced fluid indicated by a calculation tool is also the maximum mass that an object with the same volume can hold before sinking. A lifebuoy with a volume of 0.12 cubic meters displaces 120 kilograms of water in fresh water and can therefore carry exactly 120 kilograms as long as it does not sink.

Density of water and other liquids

The density of a fluid is an important factor in determining the amount of buoyancy and it is not constant. Density changes with temperature and is also affected by dissolved substances in the fluid. The density of fresh water is about 1000 kilograms per cubic meter, reaching its maximum at around 4 degrees Celsius, while decreasing to about 958 at the boiling point.

The difference you feel at the beach is due to the salt content. The average density of seawater is about 1025 kg per cubic meter, which is about 2.5 percent higher than that of fresh water. So if an object displaces enough water, it will experience a much greater buoyancy force. Air has a density of around 1.2 so the buoyancy force is usually negligible. However, with mercury having a density over 13,500 almost anything can float. A reference table for typical values is next to the calculator and can be entered directly into the Density field.

Practical applications of buoyancy

A typical example of application is shipbuilding. Shipbuilders design hulls to displace an amount of water whose weight exceeds that of the fully loaded ship. This creates a buoyancy for each tonne of iron above the waterline which supports it.

Submarines do not change the buoyancy acting on them but their own weight. When water is pumped into the ballast tanks, the submarine becomes heavier and sinks; when compressed air is used to force the water out, it becomes lighter and rises.

Hot air balloons also work on the same principle in the air. The balloon displaces a large volume of cooler outside air and the buoyancy created by this displacement supports the lighter hot air, basket and passengers.

A hydrometer is an application of this principle to measurement. A weighted float stops at a depth determined by the density of the liquid so brewers, winemakers and battery chargers can all read off the relative density directly from the scale.

Tips for accurate results:

Consider only the volume of the submerged part. A floating object displaces an amount of liquid equal to its weight; therefore, except in the case of complete immersion, the volume below water is used and not the total volume of the object.

Don't round the density values. Density changes with temperature and salinity. If you're trying to calculate a precise force, then the difference between 1000 and 1025 actually matters. Gravity also varies from about 9.78 at the equator to 9.83 at the poles, but for everyday calculations, 9.81 is a good standard value.