Buoyant Force Calculator

Buoyant Force Calculator: Find Buoyancy With Steps

This free Buoyant Force Calculator calculates the upward force exerted by water, oil, air, or another fluid on an immersed object. Choose whether you need buoyant force, displaced volume, or fluid density. Enter the known values, select convenient units, and the calculator converts them to SI units before applying Archimedes' principle. The answer panel also shows the mass of displaced fluid, while the live diagram places the density, volume, gravity, and force values beside the object in the liquid.

Use this buoyancy calculator for physics homework, fluid mechanics revision, laboratory work, boat and submarine examples, or basic engineering estimates. It uses the submerged volume rather than automatically assuming an object is fully underwater. That distinction matters: a floating object usually displaces only part of its physical volume, whereas a completely submerged object displaces a fluid volume equal to its whole volume.

Buoyant Force Formula: Fb = rho x g x V

The buoyant force formula is Fb = rho x g x V. Fb is buoyant force in newtons (N), rho is the density of the surrounding fluid in kilograms per cubic metre (kg/m3), g is gravitational acceleration in metres per second squared (m/s2), and V is the volume of fluid displaced in cubic metres (m3). Since rho x V is the mass of displaced fluid, multiplying by g gives that fluid's weight. Archimedes' principle says the upward buoyant force has exactly this magnitude.

The same relationship can be rearranged. To find displaced volume, use V = Fb/(rho x g). To find fluid density, use rho = Fb/(g x V). These forms are useful in problems about hydrometers, flotation tests, unknown liquids, and volume displacement. Keep the quantities in compatible units. For example, use 1000 kg/m3 for water and 0.02 m3 for 20 litres, not 20 m3.

How to Calculate Buoyant Force

First identify the fluid, because buoyancy depends on fluid density rather than the density of the object alone. Fresh water is approximately 1000 kg/m3, while sea water is often about 1025 kg/m3. Next find the volume below the fluid surface. For a fully submerged solid, use its total volume. For a floating block, boat, or ice cube, use only the portion of volume that is submerged. Finally multiply fluid density, gravitational acceleration, and displaced volume.

For example, a fully submerged object displaces 0.02 m3 of fresh water. Using rho = 1000 kg/m3 and g = 9.80665 m/s2, Fb = 1000 x 9.80665 x 0.02 = 196.133 N. The displaced-water mass is 1000 x 0.02 = 20 kg, and its weight is about 196.133 N. The calculator begins with these values, so its worked solution and labelled visual provide a ready-to-follow example.

Archimedes' Principle Explained

Archimedes' principle states that an object partly or fully immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. It is not necessary for the object to float. A stone at the bottom of a pool still experiences buoyancy, although its weight is greater than the upward force and the ground provides the remaining support. A spring balance holding a submerged object reads less than it does in air because buoyancy reduces the supporting force needed.

The principle applies to liquids and gases. Air provides a small buoyant force on everyday objects, while a large balloon can displace enough air to obtain a useful upward force. Water provides much more buoyancy than air for the same displaced volume because water is far denser. This is why a ship needs a huge hull volume to float in water, while a hot-air balloon needs an enormous envelope to lift in air.

Floating, Sinking, and Neutral Buoyancy

An object floats at rest when its buoyant force equals its total weight. It settles at a depth where it has displaced enough fluid for Fb to match its weight. Its average density is then lower than the surrounding fluid density. A wooden block floats because it needs to submerge only enough volume to displace water with the same weight as the block. The rest remains above the surface.

If an object is denser than the fluid, its weight is larger than the maximum buoyant force available when fully submerged, so it tends to sink. If average object density equals fluid density, the object can be neutrally buoyant: when fully submerged, its weight and buoyant force balance. Submarines use ballast systems to change average density and control depth. Shape matters because it changes volume and displaced fluid, but the force calculation always starts with rho, g, and V.

Buoyant Force Units and Conversions

The standard buoyancy unit is the newton. One newton is the force needed to accelerate one kilogram by one metre per second squared. This calculator also accepts kilonewtons and pounds-force. It supports fluid density in kg/m3, g/cm3, g/mL, and lb/ft3, plus volume in cubic metres, litres, millilitres, cubic centimetres, and cubic feet. It converts your input to SI values internally, then converts the result to the selected output unit.

Useful checks are 1 g/mL = 1 g/cm3 = 1000 kg/m3, and 1 litre = 0.001 m3. A 1-litre volume of fresh water has a mass close to 1 kg, so its buoyant force is close to 9.81 N. This quick benchmark makes it easier to spot a factor-of-one-thousand mistake. Always state the unit alongside the numerical answer, especially when mixing laboratory and engineering measurements.

Buoyancy Worked Examples

Suppose a 5-litre object is completely under fresh water. Convert 5 L to 0.005 m3. Then Fb = 1000 x 9.80665 x 0.005 = 49.033 N. If the object weighs 35 N, the upward force exceeds the downward weight, so it will rise until less of it is submerged. At floatation, it will displace water weighing 35 N, or about 3.57 kg of water.

For a second example, a sensor experiences a buoyant force of 24.52 N while submerged in water. Its displaced volume is V = 24.52/(1000 x 9.80665), approximately 0.0025 m3, which is 2.5 L. These examples show why use of submerged volume is essential. A hollow object may have a much larger external volume than the material used to make it, and it is its external submerged volume that displaces fluid.

Applications of Buoyant Force

Buoyancy explains ships, life jackets, floating bridges, submarines, hydrometers, fish swim bladders, scuba diving, and hot-air balloons. Naval architects shape hulls to displace enough water for the vessel, fuel, cargo, and passengers. Hydrometers float at different depths in liquids of different density, turning the same principle into a measurement tool. Divers adjust buoyancy with air in a buoyancy-control device so they can descend, hover, or surface safely.

In science and manufacturing, buoyancy can affect weighing accuracy, density measurement, and level sensing. A force or mass measured in air differs slightly from its vacuum value because air pushes upward. In industrial systems, pressure, temperature, dissolved gas, and fluid composition can change density. Use measured or approved design values for important decisions rather than relying solely on typical density figures.

Accuracy and Safety Notes

For an accurate calculation, use the density at the relevant temperature and condition. Water density changes modestly with temperature, and sea water varies with salinity. Gases vary far more with temperature and pressure. Make sure the volume is actually displaced, not merely the internal capacity of a container. If the object traps air, its outside submerged shape determines the displaced volume. Waves and motion create additional dynamic forces that this static buoyancy formula does not include.

Buoyancy calculations are educational estimates, not a substitute for marine, diving, lifting, or safety engineering. Water entries, overloaded vessels, pressurised systems, and diving operations involve hazards beyond static force. Follow local regulations and qualified professional procedures. For classroom questions, show the formula, substituted SI values, calculation, final unit, and a brief statement about whether the buoyant force is greater than, less than, or equal to the object's weight.

Buoyant Force Calculator FAQ Summary

Use Fb = rho x g x V to calculate the upward buoyant force. rho is fluid density, g is gravitational acceleration, and V is the displaced or submerged volume. An object floats when buoyant force equals its weight, sinks when its weight exceeds available buoyancy, and is neutrally buoyant when both forces match while fully submerged. Use the volume below the fluid surface, convert units consistently, and use a realistic fluid-density value.