About

Archimedes' principle states that the buoyant force F_b acting on a submerged object equals the weight of the displaced fluid. Miscalculating this force leads to capsized vessels, failed pontoon designs, and incorrect ballast estimates. The relationship is deceptively simple - F_b = ρ ⋅ V ⋅ g - yet errors creep in through unit mismatches (cm³ vs. m³ alone introduces a factor of 10⁶) and incorrect density assumptions for real fluids. This calculator applies the standard formulation with proper unit handling and also derives apparent weight and submersion percentage.

The tool assumes a uniform, incompressible fluid and a rigid body. It does not account for surface tension effects relevant at capillary scales, nor for compressibility corrections needed below approximately 1000 m ocean depth. For partially submerged objects at equilibrium, the submerged volume fraction equals ρ_obj ÷ ρ_fluid. Pro tip: when working with seawater, use 1025 kg/m³ rather than the commonly rounded 1000 - that 2.5% difference compounds across hull-scale volumes.

Formulas

The buoyant force is derived from Archimedes' principle. The upward force exerted by the fluid on the submerged object equals the gravitational force on the volume of displaced fluid:

F_b = ρ ⋅ V ⋅ g

Where F_b is the buoyant force in N, ρ is the fluid density in kg/m³, V is the submerged volume in m³, and g is gravitational acceleration in m/s² (standard: 9.80665).

The apparent weight of the submerged object is the difference between its true gravitational weight and the buoyant force:

W_app = W_obj − F_b = m ⋅ g − ρ ⋅ V ⋅ g

Where W_app is the apparent weight in N, m is the object mass in kg, and W_obj is the true weight.

For an object floating at equilibrium, the fraction of volume submerged is determined by the density ratio:

V_subV_total = ρ_objρ_fluid

An object floats when ρ_obj < ρ_fluid, is neutrally buoyant when ρ_obj = ρ_fluid, and sinks when ρ_obj > ρ_fluid.

Reference Data

Fluid	Density ρ (kg/m³)	Temperature (°C)	Notes
Pure Water	998	20	Standard reference fluid
Seawater	1025	15	Average ocean salinity 3.5%
Mercury	13546	20	Densest common liquid
Olive Oil	913	20	Cooking and industrial
Ethanol	789	20	Common solvent
Glycerin	1261	20	Viscous, dense organic
Gasoline	720	15	Petroleum fuel
Diesel Fuel	850	15	Heavier petroleum fuel
Milk (Whole)	1030	20	Slightly denser than water
Honey	1420	20	High viscosity, high density
Acetone	784	20	Low-density solvent
Sulfuric Acid (conc.)	1840	20	98% concentration
Liquid Nitrogen	808	−196	Cryogenic fluid
Liquid Helium	125	−269	Lightest liquid known
Kerosene	810	15	Jet fuel / heating oil
Crude Oil	870	15	Variable by source
Blood (Human)	1060	37	Body temperature reference
Turpentine	870	20	Paint solvent
Bromine	3103	20	Dense halogen liquid
Carbon Tetrachloride	1590	20	Historic cleaning solvent
Dead Sea Water	1240	20	Salinity ~34%
Air (sea level)	1.225	15	Gas buoyancy (balloons)
Helium Gas (1 atm)	0.164	20	Lighter-than-air applications
Chloroform	1490	20	Dense organic solvent
Propane (liquid)	493	25	Pressurized LPG

Frequently Asked Questions

Temperature changes fluid density. Water at 4 °C has maximum density (999.97 kg/m³), but at 80 °C drops to approximately 971.8 kg/m³. This 2.8% reduction directly reduces F_b proportionally. If your application involves heated fluids, adjust the density value manually using published density-temperature tables.

Yes. Enter only the submerged volume, not the total object volume. For a floating object at equilibrium, the submerged volume equals V_total × (ρ_obj ÷ ρ_fluid). If you provide the object mass, the calculator determines whether the object floats or sinks and computes the submerged percentage automatically.

The value 9.80665 m/s² is the standard acceleration of gravity defined by the 3rd General Conference on Weights and Measures (CGPM, 1901). The rounded 9.81 introduces a 0.034% error that compounds in large-scale engineering calculations. You can override this field for location-specific gravity - for example, 9.832 at the poles or 9.780 at the equator.

Dissolved substances increase fluid density. Ocean salinity of 3.5% raises water density from 998 to 1025 kg/m³. The Dead Sea at 34% salinity reaches 1240 kg/m³. Use a hydrometer reading or published data for the specific solution and enter the measured density in the custom density field.

Buoyant force (F_b) is the upward force from the fluid. Apparent weight (W_app) is what a scale would read while the object is submerged: W_app = mg − F_b. A negative apparent weight means the object would accelerate upward (floats). Zero apparent weight indicates neutral buoyancy - the principle used in astronaut training pools.

No. Archimedes' principle depends solely on displaced volume, not shape. A 1 m³ cube and a 1 m³ sphere experience identical buoyant force in the same fluid. Shape affects drag and stability (metacentric height), but not the static buoyant force. This calculator addresses the static case only.