Buoyant Force Calculator and Formula Explained

This buoyant force calculator estimates the upward force a fluid exerts on an immersed object. Enter the fluid density, the volume of fluid displaced, and gravitational acceleration; the result is the buoyant force in newtons, with the displaced volume also shown in cubic metres.

Formula

Archimedes’ principle says the buoyant force on an object equals the weight of the fluid it displaces:

F_b = ρ × V_d × g

• F_b is buoyant force, in newtons (N).
• ρ (rho) is the fluid’s density, in kilograms per cubic metre (kg/m³).
• V_d is the volume of fluid displaced, in cubic metres (m³).
• g is gravitational acceleration, in metres per second squared (m/s²). Near Earth’s surface, 9.81 m/s² is a common approximation.

The calculator’s second output repeats the displaced fluid’s weight, which is equal to the buoyant force under the same density and gravity assumptions. For fresh water, 1,000 kg/m³ is a useful approximate density; actual density varies with temperature and dissolved substances.

Worked Example

Using the calculator’s defaults—water density 1,000 kg/m³, displaced volume 0.01 m³, and gravity 9.81 m/s²:

1. Multiply density by displaced volume: 1,000 × 0.01 = 10 kg of displaced water.
2. Multiply that mass by gravity: 10 × 9.81 = 98.1 N.
3. Round to the calculator’s two decimal places: buoyant force = 98.10 N.

The displaced fluid’s weight is also 98.10 N. A volume of 0.01 m³ is 10 litres, so this result describes the upward force from displacing 10 litres of water under the stated assumptions.

How to Find Displaced Volume

The calculation is straightforward once you know how much fluid the object displaces. For a fully submerged object, that volume is generally the object’s submerged external volume. For a floating object, use only the portion below the fluid surface: the fluid displaced is not necessarily equal to the object’s total volume.

• Regular shapes: Calculate the submerged volume from dimensions. For a rectangular block, multiply submerged length × width × height, using consistent units.
• Irregular objects: In a suitable container, the change in fluid level can indicate displaced volume. A graduated container may be convenient for small objects.
• Floating objects: Find the submerged volume from the amount of fluid displaced, or measure it from the submerged geometry. The object settles until buoyancy balances its weight, if it is freely floating at rest.

Keep volume units consistent with density. If density is in kg/m³, enter volume in m³. For example, 1 litre is 0.001 m³, and 1 cm³ is 0.000001 m³. Entering 10 litres as 10 rather than 0.01 would make the calculated force 1,000 times too large.

Reading the Result: Floating and Sinking

Buoyant force is the fluid’s upward force, not automatically the object’s total weight or the force an underwater scale will display. Compare buoyancy with the object’s weight, W = m × g, where m is the object’s mass in kilograms:

• If buoyant force is greater than weight, the net force is upward, so the object accelerates upward until conditions change.
• If buoyant force is less than weight, the net force is downward, so it tends to sink.
• If the forces balance, the object can remain at rest at that depth or float in equilibrium.

A freely floating object displaces a fluid weight equal to its own weight. This is why a large, hollow vessel can float even if its material is denser than water: its overall average density, including enclosed air and structure, can be low enough that it displaces its weight before being fully submerged. The displaced volume is the volume of fluid pushed aside, not the volume of fluid that enters the object.

Units, Fluid Choices, and Measurement

The calculator uses SI units, but the same principle works in US customary units. In SI, density is commonly kg/m³, volume m³, and force newtons. In US customary calculations, density may be expressed as pounds-force per cubic foot (lbf/ft³); multiplying by displaced volume in ft³ gives buoyant force in lbf. Do not combine a mass density such as lbm/ft³ with a force calculation without accounting for gravity and the unit system.

Density depends on the fluid. Seawater is generally denser than fresh water, so an object displacing the same volume of seawater experiences more buoyant force. For more precise work, use a density appropriate to the fluid’s composition and temperature. The calculator treats density as constant throughout the displaced volume, which is a good approximation in many ordinary situations but may not suit fluids with strong density gradients.

Common Calculation Mistakes and Limits

• Using total volume for a partially submerged object: Only submerged volume determines displacement.
• Mixing units: Convert litres, cubic centimetres, feet, or gallons to units compatible with the entered density. A US gallon and an imperial gallon are different volumes.
• Confusing mass with force: Kilograms measure mass; newtons measure force. Multiply mass by gravitational acceleration to obtain weight in newtons.
• Assuming the result is a scale reading: Apparent weight in a fluid is related to weight minus buoyant force, but a scale arrangement can involve other forces or supports.
• Rounding too early: Keep extra digits during intermediate steps, then round the final value to a precision appropriate for the measurements.

This simple formula calculates static buoyancy from density, displaced volume, and gravity. It does not by itself model fluid flow, drag, waves, surface tension, changing immersion, or motion. A moving object can experience additional forces, and the density or displaced volume may vary over time.

Frequently Asked Questions

What is the buoyant force formula?
Buoyant force equals fluid density multiplied by displaced volume and gravitational acceleration: F_b = ρV_dg.

How do I calculate buoyant force in water?
Use water’s density in kg/m³, the submerged or displaced volume in m³, and gravity in m/s². For a rough fresh-water estimate, density is about 1,000 kg/m³ and gravity about 9.81 m/s².

Is buoyant force the same as an object’s weight?
No. Buoyant force is the upward force from displaced fluid; weight is the downward gravitational force on the object. They are equal for an object floating freely at rest, but not in every situation.

Does a floating object displace its full volume?
Not usually. It displaces the volume of fluid corresponding to its submerged portion. The displaced fluid’s weight equals the floating object’s weight when it is in equilibrium.

What happens to buoyant force in salt water?
For the same displaced volume and gravity, a denser fluid produces a greater buoyant force. Since seawater is generally denser than fresh water, it usually provides more buoyancy for the same submerged volume.

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in rho | Fluid density | kg/m^3 | 1000 | 0
in V | Displaced volume | m^3 | 0.01 | 0
in g | Gravitational acceleration | m/s^2 | 9.81 | 0
out F | Buoyant force | N | rho * V * g | 2
out W | Displaced fluid weight | N | rho * V * g | 2