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 displaced fluid—Archimedes' principle. The apparent (immersed) weight is the dry weight minus this buoyant force: W_app = W − ρ_fluid × V × g.
This calculator computes the exact buoyant force, apparent weight, and specific gravity for any object in any fluid. Choose from nine fluid presets—from air (1.225 kg/m³) to mercury (13,534 kg/m³)—or enter a custom density. The adjustable immersion slider lets you analyze partial submersion.
The force-balance visual makes the physics intuitive: see gravity pulling down, buoyancy pushing up, and the net force. The nine-fluid comparison table instantly shows whether your object floats or sinks in each fluid—critical for material identification by density testing, marine engineering, and fluid mechanics. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Buoyancy calculations are essential in marine engineering, submarine design, ROV operations, diving ballast, density measurement (hydrostatic weighing), and fluid mechanics coursework.
The multi-fluid comparison is uniquely practical—see at a glance whether your object floats in oil but sinks in water, or floats in mercury but sinks in glycerin. The force-balance diagram makes classroom demonstrations visual and intuitive.
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 |
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).