Calculation
FA = ρ·g·V
Buoyancy force equals the weight of the displaced fluid, regardless of the submerged body's shape, mass or material.
Dubbel Mechanik B 5 Hydrostatik, Gl. (5): FA = ρ·g·V (Archimedes)
Buoyancy force via Archimedes' principle
Buoyancy force equals the weight of the displaced fluid, regardless of the submerged body's shape, mass or material.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Buoyancy force FA — Upward force the fluid exerts on the submerged body.
- Fluid density ρ — Density of the displaced fluid; water at 4 °C is exactly 1,000 kg/m³.
- Gravitational acceleration g — Local gravitational acceleration, about 9.81 m/s² near sea level.
- Displaced volume V — Volume of the fully submerged part of the body, which displaces the fluid.
Example
ρ=1,000 kg/m³, g=9.81 m/s² and V=10 l (0.01 m³) give FA≈98.07 N.
Assumptions and limits
Fully submerged, rigid body in a homogeneous fluid under gravity; surface tension, flow forces and partially submerged (floating) bodies with an equilibrium condition are excluded.
Understand Buoyancy force via Archimedes' principle
This calculator determines the static buoyancy force on a fully submerged body, one of the oldest and most fundamental principles of fluid mechanics.
What does this quantity describe?
Per Archimedes, buoyancy force equals the weight of the fluid displaced by the body: FA=ρ·g·V, where V is displaced volume and ρ the fluid's density.
Formula and variables
FA = ρ·g·V
FA = ρ·g·V
| Symbol / input | Meaning |
|---|---|
| Buoyancy force FA | Upward force the fluid exerts on the submerged body. |
| Fluid density ρ | Density of the displaced fluid; water at 4 °C is exactly 1,000 kg/m³. |
| Gravitational acceleration g | Local gravitational acceleration, about 9.81 m/s² near sea level. |
| Displaced volume V | Volume of the fully submerged part of the body, which displaces the fluid. |
Choose the inputs correctly
ρ is the density of the fluid the body is submerged in, g gravitational acceleration and V the volume displaced by the body.
How to use the calculator
Take ρ from material tables (water 1,000 kg/m³, seawater about 1,025 kg/m³, air about 1.2 kg/m³), compute V from the geometry of the submerged part.
Worked example
ρ=1,000 kg/m³, g=9.81 m/s² and V=10 l (0.01 m³) give FA≈98.07 N.
Understand the result and units
Buoyancy force depends only on displaced volume and fluid density, not on the body's mass or material; whether a body floats or sinks is decided by comparison with its weight force.
ρ is a density, g an acceleration and V a volume. FA is output as a force.
Typical applications
Sizing floats, submerged bodies and ballast tanks, estimating weight reduction of submerged components, and fundamental physics teaching.
Assumptions, limits and common mistakes
Fully submerged, rigid body in a homogeneous, still fluid; surface tension, flow forces and the floating case with equilibrium between buoyancy and weight (only partially submerged) are not included.
Common mistake: Do not use the total volume of a partially submerged body; V is only the submerged portion.
Frequently asked questions
What is “Buoyancy force via Archimedes' principle” used for?
Sizing floats, submerged bodies and ballast tanks, estimating weight reduction of submerged components, and fundamental physics teaching.
Where do the input values come from?
ρ is the density of the fluid the body is submerged in, g gravitational acceleration and V the volume displaced by the body.
What does the result not cover?
Fully submerged, rigid body in a homogeneous, still fluid; surface tension, flow forces and the floating case with equilibrium between buoyancy and weight (only partially submerged) are not included.