About

Archimedes' principle states that any body wholly or partially submerged in a fluid experiences an upward buoyant force F_b equal to the weight of the fluid it displaces. Miscalculating buoyancy leads to structural failures in marine engineering, incorrect ballast in submarines, and flawed density measurements in materials science. This calculator computes buoyant force as F_b = ρ_f ⋅ V ⋅ g, determines apparent weight, displaced fluid mass, and whether an object will float, sink, or remain neutrally buoyant. It uses standard gravity g = 9.80665 m/s² per ISO 80000-3.

The tool assumes incompressible, homogeneous fluids and rigid, uniformly dense objects. Results approximate real-world behavior. Surface tension, viscosity, and turbulent drag are not modeled. For partially hollow or composite objects, use the effective (average) density. Pro tip: in salt water, buoyancy increases roughly 2.5% compared to fresh water. That margin matters for ship loading calculations.

Formulas

The buoyant force equals the weight of displaced fluid:

F_b = ρ_f ⋅ V ⋅ g

The gravitational weight of the object:

W = ρ_o ⋅ V ⋅ g

The apparent weight when submerged:

W_app = W − F_b = (ρ_o − ρ_f) ⋅ V ⋅ g

For a floating object, the submerged volume fraction:

V_subV = ρ_oρ_f

Where: ρ_f = fluid density kg/m³, ρ_o = object density kg/m³, V = object volume m³, g = gravitational acceleration = 9.80665 m/s², F_b = buoyant force N, W = weight N, W_app = apparent weight N.

Reference Data

Material	Density kg/m³	Behavior in Fresh Water
Balsa Wood	160	Floats (84% above surface)
Cork	240	Floats (76% above surface)
Pine Wood	510	Floats (49% above surface)
Oak Wood	750	Floats (25% above surface)
Ice	917	Floats (8.3% above surface)
HDPE Plastic	955	Floats (4.5% above surface)
Fresh Water	998	Neutral (reference fluid)
Seawater	1025	Sinks in fresh water
PVC	1400	Sinks
Bone (Human)	1900	Sinks
Concrete	2400	Sinks
Glass	2500	Sinks
Aluminum	2700	Sinks
Granite	2750	Sinks
Titanium	4507	Sinks
Iron / Steel	7874	Sinks
Copper	8960	Sinks
Silver	10490	Sinks
Lead	11340	Sinks
Mercury (Liquid)	13534	Sinks
Tungsten	19250	Sinks
Gold	19320	Sinks
Platinum	21450	Sinks
Osmium	22590	Sinks (densest natural element)

Frequently Asked Questions

When ρ_o = ρ_f, the buoyant force exactly equals the gravitational weight. The net force is zero, producing neutral buoyancy. The object remains at whatever depth it is placed. Submarines exploit this by adjusting ballast tank water volume to match average hull density to surrounding seawater density.

Fluid density varies with temperature. Fresh water reaches maximum density at 3.98 °C (999.97 kg/m³). At 25 °C, it drops to roughly 997 kg/m³. For precise marine or industrial calculations, use the density at operating temperature. This calculator accepts custom density values to account for temperature.

Yes. When the object density is less than the fluid density, the calculator determines the submerged volume fraction as ρ_o ÷ ρ_f. For example, ice (917 kg/m³) in fresh water (998 kg/m³) submerges 91.7%, leaving 8.3% above the waterline.

Use the effective (average) density: total mass divided by total outer volume including cavities. A steel ship hull has an average density far below 7874 kg/m³ because the enclosed air volume is enormous. This is why steel ships float despite steel itself being nearly 8 times denser than water.

No. Archimedes' principle depends only on displaced volume, not shape. A sphere and a cube of identical volume and identical fluid experience the same buoyant force. Shape affects drag, stability, and metacentric height, but not the magnitude of F_b.

The calculator uses the exact formula F_b = ρ_f ⋅ V ⋅ g with g = 9.80665 m/s² (standard gravity). Limitations: it assumes incompressible fluid, uniform density, and static conditions. For compressible fluids (deep ocean), high-pressure environments, or non-Newtonian fluids, additional correction factors are required.