Buoyant Force Calculator - Archimedes Principle Solver

The buoyant force calculator turns a fluid density, a submerged volume, and a gravitational acceleration into the upward force a fluid exerts on a submerged or floating body. It applies Archimedes' principle directly, so the same three inputs produce the buoyant force, the displaced fluid mass, and the equivalent weight on one screen.

• • Lab and classroom buoyancy problems: Solve a textbook Archimedes problem in seconds, with the displaced fluid mass shown as an intermediate so students see the F = rho * V * g product in order.
• • Hot air balloon envelope sizing: Check the buoyant force on a known envelope volume in air, then compare it to the weight of the balloon, basket, and payload.
• • Submarine and ballast tank design: Estimate the buoyant force on a hull or ballast volume in seawater at standard Earth gravity, or in fresh water at a different g value.
• • Floating structure and dock checks: Compute the upward force on a pontoon, dock float, or buoy when fully or partially submerged in fresh or salt water.

Most everyday buoyancy questions have three ingredients: a fluid, an object that pushes some of that fluid aside, and a gravitational field. The buoyant force calculator keeps all three ingredients visible in the input panel and reports the buoyant force next to the displaced fluid weight so the equivalence is plain.

If your fluid density is in grams per millilitre or pounds per gallon, the density calculator converts that reading into the kilograms per cubic metre units this buoyant force calculator expects.

The calculator implements Archimedes' principle as a single closed-form product: buoyant force equals fluid density times submerged volume times gravitational acceleration. The displaced fluid mass is reported as the intermediate step and the weight of displaced fluid is shown so the equivalence with the buoyant force is visible.

• rho_f: Fluid density in kilograms per cubic metre.
• V: Submerged volume of the object in cubic metres.
• g: Local gravitational acceleration in metres per second squared.
• F_b: Buoyant force on the object in newtons.
• m_disp: Mass of the displaced fluid in kilograms.
• W_disp: Weight of the displaced fluid in newtons, equal to F_b.

The arithmetic is one multiplication chain: density and volume give the displaced fluid mass, and that mass times gravity gives the weight of the displaced fluid, which by definition is the buoyant force. When the submerged volume is zero the result is exactly zero, and when either the fluid density or the gravity is zero the calculator rejects the input instead of producing a misleading zero.

According to Wikipedia (Archimedes' principle), the buoyant force on a body equals the weight of the fluid it displaces, written F_b = rho_fluid * V * g.

When the submerged object is a sphere, run the diameter through the sphere volume calculator first so the V input here is the exact ball volume rather than an estimate from callipers.

Four ideas sit underneath the buoyant force calculator. Read these once and the worked example above falls into place.

These four ideas together explain why the same object can float in one fluid and sink in another, why reducing an object's submerged volume reduces the buoyant force, and why the answer scales linearly with the local gravity.

The same principle extends to a two-liquid stack in the buoyancy experiment calculator, which back-solves an unknown upper liquid density from the same Archimedes product applied separately to the cap and dome.

Use the tool in five steps; default values reproduce the textbook 1 L object in fresh water on Earth so you can verify the workflow before plugging in your own numbers.

1. 1 Look up the fluid density: Enter the fluid density in kilograms per cubic metre. Use 1000 for fresh water at 4 degC, 1025 for typical seawater, and about 1.225 for air at sea level.
2. 2 Measure the submerged volume: Read the volume of the object below the fluid surface in cubic metres. For a fully submerged object this is the full volume; for a floating object it is the volume under the waterline.
3. 3 Set the gravitational acceleration: Use 9.80665 m/s^2 for Earth. Switch to 1.62 for the Moon, 3.71 for Mars, or 24.79 for Jupiter if the problem is set on another body.
4. 4 Run the calculation: Press Calculate or edit any field and the result updates in real time. The Buoyant Force panel shows the upward force in newtons alongside the displaced fluid mass and weight.
5. 5 Compare the buoyant force to the object's weight: Multiply the object's mass by the same gravity to get its weight. If weight exceeds the buoyant force, the object sinks; if less, it floats until enough volume is submerged to balance.

A 1 L bottle (0.001 m^3) submerged in fresh water on Earth returns a buoyant force of 9.80665 N. The same bottle on the Moon returns only 1.62 N, so an object that floats easily on Earth behaves very differently in a lower gravity.

Once the buoyant force is known, plug the weight, the buoyant force, and any applied load into the forces and newton's laws calculator to see the net force that decides whether the object rises, sinks, or hovers.

Reasons to reach for this tool instead of doing the Archimedes product by hand or relying on a memorized constant.

• • One panel for the whole Archimedes product: Fluid density, submerged volume, and gravity share a panel with the buoyant force and the displaced fluid mass, so the inputs and intermediates stay visible together.
• • Auditable for lab reports: Every output is a closed-form evaluation of F_b = rho * V * g. The same calculation can be repeated by hand on the lab sheet and checked field by field.
• • Reproduces a canonical worked example: The default values match the textbook 1 L object in fresh water, so the workflow can be verified against a known answer before plugging in your own numbers.
• • Supports non-Earth gravities: Changing the gravity input lets you read the buoyant force on the Moon, Mars, Jupiter, or any custom body without re-deriving the formula.
• • Pairs with classroom fluid mechanics: The same fluid density and submerged volume flow naturally into the Bernoulli equation and Reynolds number calculators for moving-fluid problems.
• • Handles the zero and negative edge cleanly: When the inputs force a non-physical case, the tool returns null and a clear reason instead of producing a silent zero.

The tool is intentionally narrow: it solves one specific Archimedes problem well. It does not model surface tension, viscosity, or partial-immersion stability, which would obscure the simple force product the textbook equation is designed to demonstrate.

After solving the static buoyancy problem, the same fluid density feeds a moving-fluid problem through the bernoulli equation calculator when the next lab segment covers streamline energy balances instead of static lift.

What changes the answer this calculator returns, and what it cannot capture because the model is intentionally simple.

• • It assumes a single homogeneous fluid with the density you entered. Layered fluids, thermal gradients, or gas-liquid mixtures need the buoyancy-experiment approach or a piecewise density profile instead.
• • It assumes the object is rigid and the submerged volume does not change with pressure. A compressible object at depth will have a smaller submerged volume and a smaller buoyant force than the calculator reports.

Use the tool as the backbone of an Archimedes calculation; the formula-only answer is usually well within the noise of a hand-measured submerged volume. For floating stability or ship motion you need moments and the centre of buoyancy as well, which this single-force calculator does not attempt.

As published by Wikipedia (Buoyancy), the buoyancy force on a submerged object equals the weight of the displaced fluid, written F_b = rho_f * V * g.

According to Wikipedia (Standard gravity), the standard gravity adopted by the CGPM in 1901 is 9.80665 m/s^2 and is the local g used in the buoyant force formula F_b = rho * V * g.

When the object starts to move through the fluid, the density you entered here combines with a velocity and a length scale in the reynolds number calculator to characterise the flow regime around it.