Buoyancy Calculator - Force, Volume, Density Solver

A buoyancy calculator is a fluid-mechanics tool that applies Archimedes' principle to find the upward force a fluid exerts on a fully or partially submerged object. Pick a fluid, enter the displaced volume, and the calculator returns the buoyant force in newtons, the mass of fluid displaced, and a float-or-sink verdict against an optional object weight. The same calculator also rearranges the formula to solve for the displaced volume or the fluid density when those are the unknowns.

• • Homework and lab problems: Check Archimedes-principle textbook and lab write-ups for steel blocks, ice cubes, model submarines, or floating containers.
• • Boat, raft, and pontoon design: Estimate how much buoyant force a hull needs to support a known weight in fresh water, sea water, or other liquids.
• • Diver and life-jacket checks: Confirm that a wetsuit, life jacket, or diving bell provides enough net buoyant force to keep a person at the surface.
• • Tank and process-fluid sizing: Pick a process fluid and a submerged volume, then back out the upward load on submerged sensors, floats, or piping.

Buoyancy is what keeps ships on the surface, hot-air balloons in the air, and divers bobbing back up when they stop swimming down. The buoyancy calculator keeps the physics tied to one formula, B = rho V g, so you can answer "will it float?" without re-deriving the algebra each time.

When the fluid density is given in a non-metric unit, the density calculator on the math-conversion side can convert it to kilograms per cubic metre before you enter it here.

The calculator evaluates Archimedes' principle in its SI form, B = rho * V * g, and rearranges it for the variable you selected in the Solve For menu. Standard gravity g is fixed at 9.80665 m/s^2 with an editable field for planetary or planetary-orbit comparisons.

• rho: Mass density of the surrounding fluid in kilograms per cubic metre (kg/m^3).
• V: Volume of fluid displaced by the submerged part of the object in cubic metres (m^3). For a fully submerged body, this is the full body volume.
• g: Local gravitational acceleration in metres per second squared (m/s^2). The default 9.80665 m/s^2 is the conventional standard value published by NIST for Earth surface calculations.
• B: Resulting buoyant force in newtons (N), equal to the weight of the displaced fluid.

All three solves (force, volume, density) use the same physical relationship. The mass of displaced fluid and the weight of the displaced fluid are reported in parallel so the result can be cross-checked by hand against rho * V and rho * V * g.

According to Wikipedia, the buoyant force on a body immersed in a fluid is equal to the weight of the fluid the body displaces and is given by B = rho V g.

According to NIST Special Publication 330, the conventional standard value of Earth-surface gravitational acceleration adopted for calculations is 9.80665 m/s^2, which is the default used here.

If the submerged volume is given in cubic centimetres, litres, or gallons, the volume calculator converts it to cubic metres so this calculator can read the value directly.

Four ideas behind the buoyancy calculator that are worth understanding before you trust the numbers.

These four ideas show up in every buoyancy problem. They also reappear in fluid-flow problems (Bernoulli's equation) and in straight-line motion problems (force, mass, and acceleration), so the rest of the physics calculators on this site pick up the same vocabulary in a different form.

When buoyancy turns into a moving-fluid problem, the Bernoulli equation calculator applies the related conservation-of-energy form to pressure, velocity, and elevation along a streamline.

Use the buoyancy calculator in five steps.

1. 1 Pick the unknown: Open the Solve For menu and choose Buoyant force, Displaced volume, or Fluid density. The default Buoyant force is the most common textbook case.
2. 2 Choose a fluid preset or Custom: Pick Fresh water, Sea water, Ethanol, Methanol, Vehicle gasoline, Heating oil, Fuel oil, or Sulfuric acid 95 percent to load a density value, or pick Custom and enter your own density in the rho field.
3. 3 Enter the remaining inputs: Fill the two other numeric fields needed for the chosen Solve For target. For Buoyant force you need volume and gravity; for Displaced volume or Fluid density you also need a known buoyant force.
4. 4 Optionally add an object weight: Type the weight of the object in newtons in the Object Weight field to enable the Floating Check verdict that compares B and W.
5. 5 Read the solved value and the secondary outputs: The Solved Variable shows the value of whichever variable you picked, while Mass of Displaced Fluid and Weight of Displaced Fluid give an independent cross-check in kilograms and newtons.

A 5 kg piece of foam has a weight of about 49 N on Earth. Pick Fresh water (rho = 1000), set Solve For to Displaced volume, enter 49 for the buoyant force, and the calculator returns about 0.005 m^3, which is roughly the 5 litre volume you would expect for a foam cube of density 1.

If the object weight is given in kilograms of mass, the weight converter can convert it to the newtons of force the Floating Check expects.

Practical reasons to use this buoyancy calculator instead of doing the algebra by hand.

• • One tool for three unknowns: Switch the Solve For menu to rearrange the same equation for force, displaced volume, or fluid density.
• • Fluid presets save lookups: The preset list covers water, sea water, ethanol, methanol, gasoline, heating oil, fuel oil, and sulfuric acid.
• • Auditable secondary outputs: Mass and Weight of Displaced Fluid are reported in parallel with the primary answer for a one-line hand check.
• • Optional float or sink verdict: Typing an object weight turns on a clear Object floats or Object sinks label.
• • Standard gravity with planetary override: The gravity field defaults to 9.80665 m/s^2 and accepts lower values for Mars, the Moon, or any other surface.
• • Connects to other physics calculators: The same density and volume inputs feed the wider physics cluster on the site.

When the buoyancy problem turns into a falling or rising body, the same time and acceleration values feed the kinematics motion calculator.

What changes the answer the buoyancy calculator returns, and what it cannot capture.

• • The calculator assumes a single uniform fluid density and does not model a stratified ocean with a sharp halocline or thermocline. For layered fluids, average the density or treat each layer separately.
• • Archimedes' principle applies to a static or quasi-static fluid. For a fast-moving object that pushes the fluid out of the way, the calculator does not include added-mass or drag effects.
• • The fluid preset densities are reference values for typical conditions. Real fluids shift by 1 to 5 percent with temperature and pressure changes, so use the Custom field when those shifts matter.

According to Engineering Toolbox, typical sea water has a density of about 1025 kg/m^3 at 15 deg C, and the standard table of liquid densities is the usual starting point for buoyancy problems.

When the displaced fluid weight is then used to estimate the work needed to lift the object out of the fluid, the work energy power calculator takes the resulting force times distance and reports it in joules.