Immersed Weight Calculator

About the Immersed Weight Calculator

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.

When This Page Helps

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.

How to Use the Inputs

1. Select a preset or enter the object density in kg/m³.
2. Choose a fluid from the dropdown or enter a custom fluid density.
3. Enter the object volume and select the unit (m³, cm³, L, in³, ft³).
4. Adjust the immersion percentage (100% = fully submerged).
5. View dry weight, buoyant force, apparent weight, specific gravity, and float/sink status.
6. Check the comparison table for behavior in different fluids.

Example Calculation

Tips & Best Practices

• For body composition testing (hydrostatic weighing), the "underwater weight" determines body fat percentage using Siri's equation.
• Specific gravity (SG) is dimensionless: SG = ρ_object / ρ_reference. For solids, the reference is usually water at 4 °C (1000 kg/m³).
• Objects with SG very close to 1.0 (e.g., ice at 0.917) are nearly neutrally buoyant—important for submarine ballast design.
• Temperature affects fluid density: warm water is less dense, reducing buoyancy. Ocean-going vessels sit lower in warm tropical water than in cold polar water.
• The immersion slider lets you model the waterline: at equilibrium, a floating object displaces a fluid weight equal to its own weight.

Archimedes and the Golden Crown

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.

Buoyancy in Engineering

| 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 |

Frequently Asked Questions

• What is Archimedes' principle?

  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.

• How is this used to test gold purity?

  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.

• Does shape affect buoyancy?

  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.

• What about partial immersion?

  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.

• Why does steel float as a ship but sink as a block?

  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.

• What is the center of buoyancy?

  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).