THE NUMORIX GUIDE
How to use the Buoyancy Calculator
Last reviewed September 14, 2026
What this calculator does
Archimedes' principle gives buoyant force F_b = rho V g, where the force equals the weight of the displaced fluid.
Formula and method
Archimedes' principle gives buoyant force F_b = rho V g, where the force equals the weight of the displaced fluid. The engine reports that same value separately as displaced-fluid weight.
Variables and inputs
Enter fluid density rho in kg/m^3, displaced volume V in m^3, and gravitational acceleration g in m/s^2. The defaults are water at 1,000 kg/m^3, 0.5 m^3 displaced, and 9.81 m/s^2; the result is in newtons.
Worked example
For rho = 1,000 kg/m^3, V = 0.5 m^3, and g = 9.81 m/s^2: F_b = 1,000(0.5)(9.81) = 4,905 N. The weight of the displaced fluid is also 4,905 N.
How to interpret the result
Buoyant force acts upward and is set by the volume of fluid displaced, not directly by the object's total mass. To decide whether an object floats, compare this upward force with the object's weight and consider how its submerged volume changes.
Common mistakes to avoid
Use the submerged or displaced volume rather than the object's outside volume when it is only partly submerged. Keep density in kg/m^3, volume in m^3, and gravity in m/s^2; do not compare a force in newtons with a mass in kilograms.
Assumptions and limitations
The calculation assumes a static fluid with uniform density and a known displaced volume. It does not model fluid motion, viscosity, surface tension, compressibility, body stability, or the changing immersion of a floating object, and the input component does not validate physical ranges.
Practical use and checks
The Buoyancy Calculator applies Archimedes' principle: buoyant force equals fluid density times displaced volume times gravitational acceleration. Enter water density 1,000 kg/m^3, displaced volume 0.5 m^3, and g = 9.81 m/s^2 as a check; the force should be 4,905 N. To decide whether an object floats at a particular immersion, compare that upward force with the object's weight. A positive buoyant force alone does not prove that the object will rise or remain stable. Use the submerged or displaced volume, not automatically the object's full outside volume. A hollow boat and a solid block with the same outside dimensions can displace fluid differently at equilibrium. Keep density, volume, and gravity in compatible SI units, and compare force with force rather than mass with newtons. The model assumes a static, uniform, incompressible fluid and a known displaced volume. It omits fluid motion, viscosity, surface tension, stability, waves, changing immersion, body deformation, and the effect of trapped air. Density changes with temperature and pressure in real fluids. For a vessel, pool, or underwater load decision, calculate the equilibrium immersion and center of buoyancy separately rather than treating one fixed volume as the full flotation analysis.