Calculate apparent weight and buoyant force for objects submerged in any fluid. Archimedes principle with 9-fluid comparison and force-balance visual.
When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the displaced fluid. That is Archimedes' principle, and it is why an object's apparent weight in water is smaller than its dry weight.
This calculator computes buoyant force, apparent weight, and specific gravity for an object in any fluid. You can choose from preset fluids or enter a custom density, then adjust the immersion level to model partial submersion.
The force-balance view shows gravity, buoyancy, and the net force side by side, while the fluid comparison table makes it easy to see whether the object floats or sinks in each case.
Immersed-weight calculations are useful whenever you need to know how much a fluid changes the load on an object. That includes buoyancy checks, density testing, ballast planning, and any case where the dry weight is not the weight you actually have to support in the fluid.
Buoyant Force: F_b = ρ_fluid × V_immersed × g. Apparent Weight: W_app = m × g − F_b = (ρ_object − ρ_fluid) × V × g. Specific Gravity: SG = ρ_object / ρ_fluid. Float if ρ_object < ρ_fluid (SG < 1).
Result: Apparent weight = 67.20 N (dry: 76.98 N, buoyancy: 9.78 N)
Dry weight = 7.85 × 9.81 = 77.0 N. Buoyant force = 997 × 0.001 × 9.81 = 9.78 N. Apparent weight = 77.0 − 9.78 = 67.2 N. Loses 12.7% of its weight in water.
The legendary story: King Hiero II of Syracuse asked Archimedes to determine whether his crown was pure gold without melting it. Archimedes realized that he could compare the crown's volume (by water displacement) to a known gold mass. If the crown displaced more water than the same mass of pure gold, it contained less-dense metals.
This is the principle of hydrostatic density testing, still used today for gemstones, precious metals, and archaeological artifacts.
| Application | What Buoyancy Determines | |---|---| | Ship design | Draft, freeboard, stability | | Submarine | Ballast tank volume for neutral buoyancy | | ROV/AUV | Syntactic foam volume for depth rating | | Diving | Weighting for neutral buoyancy | | Hydrometer | Fluid density from float depth | | Concrete testing | Air content by buoyancy method |
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Any object wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. F_b = ρ_fluid × V_displaced × g.
Weigh the item in air and in water. The ratio of air weight to weight loss in water gives specific gravity. Pure gold has SG ≈ 19.3; 14K gold ≈ 13.6. Fakes (tungsten-filled) have different SG.
Only the volume of fluid displaced matters, not the shape. A flat plate and a sphere of the same volume experience the same buoyant force when fully submerged.
The buoyant force equals the weight of fluid displaced by the immersed portion only. Use the immersion slider to model partially submerged objects like ships or floating logs.
A ship's hull encloses air, so the average density of the hull is less than water. A solid steel block has density 7,850 kg/m³ (>> 1,000 for water), so it sinks.
The centroid of the displaced fluid volume. For stability, the center of buoyancy must be above the center of gravity (or metacentric height must be positive).