Buoyant Force Calculator: Formula and Examples

This calculator finds the buoyant force on an object from the fluid’s density and the volume of fluid the object displaces. Enter those two values, and it returns the upward force in newtons, along with the equivalent force in pounds-force.

Formula

Archimedes’ principle gives the buoyant force as the weight of the displaced fluid:

F_b = ρ × V × g

• F_b is buoyant force, measured in newtons (N).
• ρ (rho) is the fluid density, in kilograms per cubic metre (kg/m³).
• V is the volume of fluid displaced, in cubic metres (m³). For an object fully immersed in a fluid, this is the object’s submerged volume. For a floating object, it is the volume below the fluid surface.
• g is gravitational acceleration. The calculator uses 9.80665 m/s², the standard value used for this calculation.

Since density times volume gives mass, multiplying by gravitational acceleration converts that mass into weight. In US customary units, the equivalent relationship is force in pounds-force = fluid density in pounds per cubic foot × displaced volume in cubic feet. This calculator converts its result in newtons to pounds-force (lbf).

Worked Example

Using the calculator’s default values—water density of 1,000 kg/m³ and displaced volume of 0.01 m³:

1. Multiply density by displaced volume: 1,000 kg/m³ × 0.01 m³ = 10 kg of displaced water.
2. Multiply that mass by gravitational acceleration: 10 kg × 9.80665 m/s² = 98.0665 N.
3. Round to two decimal places: the buoyant force is 98.07 N.
4. Convert to pounds-force: 98.0665 N ÷ 4.448221615 = 22.0407 lbf, or 22.04 lbf rounded to two decimals.

The force points upward. This result is the buoyant force alone; it is not necessarily the object’s net force or its apparent weight.

How Buoyancy Works

Fluid pressure increases with depth. The bottom of an immersed object is therefore pushed by greater pressure than its top, creating a net upward force. Archimedes’ principle summarizes that pressure effect: the upward buoyant force equals the weight of the fluid displaced by the object.

The calculation depends on the amount of fluid displaced, not directly on the object’s total mass or material. For a solid object fully submerged in a uniform fluid, its displaced volume is usually its external volume. If it is only partly submerged, count only the portion below the surface. A hollow object’s displacement is based on the fluid it excludes; whether water can enter openings matters to the effective displaced volume.

Choosing Density and Displaced Volume

Use the density of the fluid where the object is located, not the density of the object. Density changes with fluid type and can also vary with temperature, pressure, or concentration. For a simple estimate, a standard density for the fluid may be adequate; for precise work, use a value appropriate to its actual conditions.

• Regular shapes: Calculate the submerged geometric volume. For a rectangular section, multiply length × width × submerged height; convert the result to cubic metres.
• Irregular solid objects: A volume-displacement measurement can estimate the object’s volume if it is fully submerged and does not absorb fluid or trap air.
• Floating objects: Measure or calculate the submerged portion only. The exposed part does not displace fluid.
• Multiple fluids: If an object spans distinct layers, calculate the contribution from the volume in each fluid and add the forces: F_b = g × (ρ₁V₁ + ρ₂V₂ + …).

In US customary measurements, density may be given in lb/ft³ and volume in ft³, producing lbf directly when density is expressed as weight density. Do not treat lb/ft³ as mass density in a formula that also multiplies by gravitational acceleration. Alternatively, convert density and volume to kg/m³ and m³, then use the calculator.

Interpreting the Result

To decide whether an object rises, sinks, or remains in equilibrium, compare buoyant force with the object’s weight. If buoyant force is greater than its weight, the net force is upward; if it is smaller, the net force is downward. At rest while floating, the forces balance, so the buoyant force equals the object’s weight. This explains why a floating object displaces a quantity of fluid whose weight matches its own.

For example, the default calculation gives 98.07 N of upward force. It does not tell you whether an object will float unless you also know the object’s weight and account for any other forces. If the object is held down or attached to a support, those forces affect its equilibrium but do not change the basic buoyant-force calculation for a given displaced volume.

Common Errors and Limits

• Mixing units: The calculator expects kg/m³ and m³. A volume in litres must be divided by 1,000 to convert to m³; a volume in cm³ must be divided by 1,000,000.
• Using total volume when only part is submerged: For a partly immersed object, use the submerged volume, not its full external volume.
• Confusing force and mass: The formula returns newtons, a force unit. Kilograms measure mass. The mass of displaced fluid is ρV, but its weight is ρVg.
• Assuming density is universal: Fresh water is often approximated as 1,000 kg/m³, but the appropriate density depends on the actual fluid and conditions.

The simple formula assumes a fluid at rest and a known displaced volume and density. In rapidly moving fluids, changing fluid density, or complicated situations with trapped gas or fluid flow, additional analysis may be needed. Rounding intermediate values can also slightly alter a final result, so retain precision until the last step.

Frequently Asked Questions

What is the formula for buoyant force?
Use F_b = ρVg: fluid density multiplied by displaced volume and gravitational acceleration. The answer is a force, typically in newtons.

How do I find buoyant force on a floating object?
Find the volume below the fluid surface, then multiply it by the fluid density and gravitational acceleration. When the object is floating at rest, that buoyant force equals the object’s weight.

Does buoyant force depend on an object’s mass?
Not directly. For a specified fluid and displaced volume, buoyant force is set by the displaced fluid’s weight. The object’s mass matters when comparing buoyancy with its weight to determine its motion or floating condition.

How do I convert buoyant force from newtons to pounds-force?
Divide the force in newtons by 4.448221615. For example, 98.07 N is approximately 22.04 lbf.

Is buoyant force the same as apparent weight?
No. Apparent weight is the object’s weight minus the upward buoyant force, when those are the relevant vertical forces. Buoyant force is the upward force exerted by the fluid itself.

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in rho | Fluid density | kg/m^3 | 1000 | 0
in v | Displaced volume | m^3 | 0.01 | 0
out f | Buoyant force | N | rho * v * 9.80665 | 2
out fp | Buoyant force | lbf | f / 4.448221615 | 2