Buoyancy Calculator

Buoyancy is evaluated from Fluid Density, Submerged Volume and Object Mass. The calculation reports Buoyant Force, Buoyant Force and Mass of Displaced Fluid.

Results

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About the Buoyancy Calculator

Buoyancy is treated here as a quantitative relation between Fluid Density, Submerged Volume and Object Mass and Buoyant Force, Buoyant Force, Mass of Displaced Fluid and Net Force.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
F = ρ x V x g
F = Buoyant Force (N)
ρ = Fluid density (kg/m^3)
V = Volume of displaced fluid (m^3)
g = 9.80665 m/s^2
Object floats if: F_buoyancy > Weight (m_object x g)
Net force = F_buoyancy - Weight

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

F = ρ x V x g
F = Buoyant Force (N)
ρ = Fluid density (kg/m^3)
V = Volume of displaced fluid (m^3)
g = 9.80665 m/s^2
Object floats if: F_buoyancy > Weight (m_object x g)
Net force = F_buoyancy - Weight

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Steel Ship Hull

Inputs

fluid_density: 1025 volume: 50000 object_mass: 40000000
Buoyant Force: 502,590,812.5 N. Buoyant Force: 112,986,937.967 lbf. Mass of Displaced Fluid: 51,250,000 kg. Net Force: 110,324,812.5 N

With Fluid Density = 1,025, Submerged Volume = 50,000 and Object Mass = 40,000,000 as the stated inputs, the result is Buoyant Force = 502,590,812.5 N, Buoyant Force = 112,986,937.967 lbf and Mass of Displaced Fluid = 51,250,000 kg. Each value corresponds to the declared output fields.

Example 2: Foam Pool Float

Inputs

fluid_density: 1000 volume: 0.02 object_mass: 4
Buoyant Force: 196.133 N. Buoyant Force: 44.092 lbf. Mass of Displaced Fluid: 20 kg. Net Force: 156.906 N

With Fluid Density = 1,000, Submerged Volume = 0.02 and Object Mass = 4 as the stated inputs, the result is Buoyant Force = 196.133 N, Buoyant Force = 44.092 lbf and Mass of Displaced Fluid = 20 kg. Each value corresponds to the declared output fields.

Example 3: Submarine Neutral Buoyancy

Inputs

fluid_density: 1025 volume: 7800 object_mass: 7995000
Buoyant Force: 78,404,166.75 N. Buoyant Force: 17,625,962.323 lbf. Mass of Displaced Fluid: 7,995,000 kg. Net Force: 0 N

With Fluid Density = 1,025, Submerged Volume = 7,800 and Object Mass = 7,995,000 as the stated inputs, the result is Buoyant Force = 78,404,166.75 N, Buoyant Force = 17,625,962.323 lbf and Mass of Displaced Fluid = 7,995,000 kg. Each value corresponds to the declared output fields.

Example 4: Dock Flotation Barrels

Inputs

fluid_density: 1000 volume: 0.208 object_mass: 15
Buoyant Force: 2,039.783 N. Buoyant Force: 458.562 lbf. Mass of Displaced Fluid: 208 kg. Net Force: 1,892.683 N

With Fluid Density = 1,000, Submerged Volume = 0.208 and Object Mass = 15 as the stated inputs, the result is Buoyant Force = 2,039.783 N, Buoyant Force = 458.562 lbf and Mass of Displaced Fluid = 208 kg. Each value corresponds to the declared output fields.

Common Use Cases

  • Determine if a ship design will float
  • Calculate buoyant force on a submarine ballast tank
  • Find required volume to keep a dock float afloat