Free · Fluid mechanics calculators 💧

Buoyancy & Displaced Fluid Mass

Calculate buoyant force from submerged volume, fluid density and gravity, using fluid presets or a custom density.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A displaced volume of 0.01 m³ in fluid of density 1,000 kg/m³ displaces 10 kg and produces 98.0665 N of buoyancy at standard gravity.

Displaced mass = fluid density × displaced volume; buoyant force = displaced mass × gravity

Worked example

Enter these known values and leave the other values blank.

Fluid preset or custom density
Custom
Density of displaced fluid
1000 kg/m³
Submerged / displaced volume
0.01 m³
Gravitational acceleration
1 g
Upward buoyant force
98.07 N
Mass of displaced fluid
10 kg

Assumptions and limitations

  • Use only the volume actually submerged and displacing fluid. It may be smaller than the object’s whole volume.
  • Density and gravity are uniform through the displaced region. Presets are illustrative densities; composition, temperature and pressure can change real density.
  • All inputs describe positive magnitudes. The initial metric gravity of 1 g equals 9.80665 m/s²; the imperial starting value is rounded.
  • Buoyant force is not net force. Subtract object weight and account for other forces separately to determine motion.

Common questions

Does a sinking object still have buoyancy?

Yes. The fluid still pushes upward; sinking means that upward force is insufficient to balance the other forces.

Which density goes into the formula?

Use the surrounding fluid’s density. The object’s density is a separate property.

References

Bookify requires positive gravity, consistent with the positive displaced mass and buoyant-force model. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor. The pound-force uses the exact international pound and standard gravity instead of the rounded captured factor. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference.

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