About

Archimedes' principle states that the buoyant force F_b acting on a submerged object equals the weight of the fluid it displaces: F_b = ρ_f ⋅ V ⋅ g. A miscalculation of displaced volume or fluid density leads to incorrect load predictions in marine engineering, submersible design, and hydrometer calibration. This calculator computes buoyant force, net vertical force, apparent weight, and submerged fraction for any object - fluid pair. It assumes a rigid body fully or partially immersed in a homogeneous, incompressible fluid at rest. Results lose accuracy for compressible fluids, non-uniform density distributions, or objects undergoing plastic deformation under hydrostatic pressure.

Formulas

The buoyant force exerted on a submerged body by a fluid at rest:

F_b = ρ_f ⋅ V ⋅ g

The gravitational weight of the object:

W = ρ_o ⋅ V ⋅ g

Net vertical force (positive upward):

F_net = F_b − W = (ρ_f − ρ_o) ⋅ V ⋅ g

Apparent weight when fully submerged:

W_app = W − F_b

Fraction of volume submerged when floating (ρ_o < ρ_f):

f_sub = ρ_oρ_f

Where: ρ_f = fluid density kg/m³, ρ_o = object density kg/m³, V = object volume m³, g = gravitational acceleration m/s² (default 9.80665).

Reference Data

Material	Density kg/m³	Notes
Balsa Wood	160	Lightest commercial wood
Cork	240	Closed-cell natural polymer
Pine Wood	510	Softwood average
Oak Wood	750	Hardwood average
Ice (0 °C)	917	Floats in liquid water
HDPE Plastic	955	High-density polyethylene
Water (4 °C)	1000	Maximum density reference
Concrete	2400	Unreinforced average
Aluminum	2700	Alloy 6061 typical
Titanium	4507	Grade 5 (Ti-6Al-4V)
Steel (Mild)	7850	AISI 1020
Copper	8960	C11000 ETP
Lead	11340	Pure, cast
Gold	19320	24-karat pure
Tungsten	19250	Sintered

Fluid	Density kg/m³	Conditions
Air (sea level)	1.225	15 °C, 1 atm
Ethanol	789	20 °C
Gasoline	750	15 °C average
Olive Oil	913	25 °C
Fresh Water	998	20 °C
Seawater	1025	15 °C, 3.5% salinity
Milk (Whole)	1030	20 °C
Dead Sea Water	1240	~34% salinity
Glycerin	1261	25 °C
Sulfuric Acid	1840	Concentrated, 25 °C
Mercury	13534	25 °C

Frequently Asked Questions

Water density varies from approximately 999.84 kg/m³ at 0 °C to 958.4 kg/m³ at 100 °C. A 40 °C temperature swing can shift buoyant force by roughly 2-3%. For precision work in oceanography or industrial tank design, use the measured fluid density at operating temperature rather than the standard 998 kg/m³ value.

A submerged fraction exceeding 100% means the object is denser than the fluid and will sink. The ratio ρ_object / ρ_fluid exceeds 1, so the object cannot displace enough fluid to support its own weight. The displayed percentage indicates how much denser the object is relative to the fluid.

No. Archimedes' principle depends on displaced volume, not shape. A solid steel sphere and a solid steel cube of equal volume experience identical buoyant forces in the same fluid. Shape matters for drag and stability (metacentric height), but not for static buoyancy magnitude. Hollow objects (e.g., ships) float because their effective average density (total mass divided by outer hull volume) is less than the fluid density.

Yes. Set the fluid density to air at your altitude (1.225 kg/m³ at sea level, 15 °C) and the object density to the average density of the balloon (gas mass plus envelope mass divided by total volume). The same Archimedes equation governs aerostatic lift. Note that gas compressibility makes density altitude-dependent, which this static calculator does not model.

Apparent weight equals W − F_b and represents what a submerged scale would read: always non-negative for sinking objects. Net force equals F_b − W and indicates the direction of motion: positive means the object accelerates upward (floats), negative means it accelerates downward (sinks), and zero means neutral buoyancy. They are equal in magnitude but opposite in sign.

The value 9.80665 m/s² is the ISO 80000-3 standard gravity. Actual local gravity ranges from about 9.764 m/s² at the equator (high altitude) to 9.834 m/s² at the poles. For most engineering purposes the default is sufficient. For metrology-grade calculations, input your local measured value.